What angels and fallen angels were named in the Bible and what are they responsible for? I've also heard of works of theologians on that matter, can someone provide some references?
There are only two angels mentioned by name in Scripture:
Other Angels appear in the OT (One to Manoah in Judges to announce the birth of Samson, three to Abraham in Genesis), but they are unnamed.
An angel has only one job, as implied by the name - they deliver messages.
When they are not doing this job, they are usually in the presence of the Lord, praising him and announcing his glory (Isaiah 6, Revelation)
Debatedly, the only fallen angel is Lucifier in Isaiah 14 - the "Star of Morning" who is the Devil.
One could also describe "Legion" as a demon in Luke 5 (at Genesseret), but that isn't a proper name, rather a collection of Demons.
@Affable Geek's right, but doesn't mention the Archangel Raphael as his tradition doesn't consider the book of Tobit scripture.
Since Catholics and Orthodox include this book, he's also one of the angels named in the Bible. His name means God Heals and he's the one who took Tobias on his journey and helped him heal his father's blindness. He's actually pretty awesome.
Also, in Catholic tradition (and other traditions), it was two angels who visited Abraham and Sarah, along with God.
I have been rereading many texts I thought I knew well, and finding new surprises. Revelation 9:11 (ESV) says: "They have as king over them the angel of the bottomless pit. His name in Hebrew is Abaddon, and in Greek he is called Apollyon." And, we may not know until all things are revealed what the true roles of the angels actually are. But here is another named angel (other than Michael, Gabriel and Lucifer).
The source to the list of fallen presented from A-Z comes from "A Dictionary of Angels including the fallen angels" by Gustav Davidson and is considered one of the preminent sources on angels. The word "demon" comes from The words dæmon or daimôn which are Latinized versions of the Greek "δαίμων", a reference to the daemons of ancient Greek religion and mythology, as well as later Hellenistic religion and philosophy. Daemons are benevolent or benign nature spirits, beings of the same nature as both mortals and gods, similar to ghosts, chthonic heroes, spirit guides, forces of nature or the gods themselves (see Plato's Symposium). Walter Burkert suggests that unlike the Christian use of demon in a strictly malignant sense, “[a] general belief in spirits is not expressed by the term daimon until the 5th century when a doctor asserts that neurotic women and girls can be driven to suicide by imaginary apparitions, ‘evil daimones’. How far this is an expression of widespread popular superstition is not easy to judge… On the basis of Hesiod's myth, however, what did gain currency was for great and powerful figures to be honoured after death as a daimon…”  Daimon is not so much a type of quasi-divine being, according to Burkert, but rather a non-personified “peculiar mode” of their activity.
In Hesiod's Theogony, Phaëton becomes an incorporeal daimon or a divine spirit but, for example, the ills released by Pandora are deadly gods, keres, not daimones. From Hesiod also, the people of the Golden Age were transformed into daimones by the will of Zeus, to benevolently serve mortals as their guardian spirits; “good beings who dispense riches…[nevertheless], they remain invisible, known only by their acts”. The daimon of venerated heroes, were localized by the construction of shrines, so as not to restlessly wander, and were believed to confer protection and good fortune on those offering their respects.
Characterizations of the daemon as a dangerous, if not evil, lesser spirit were developed by Plato and his pupil Xenocrates,[dubious ] and later absorbed in Christian patristic writings along with Neo-Platonic elements.
In the Old Testament, evil spirits appear in the book of Judges and in Kings. In the Greek translation of the Septuagint, made for the Greek-speaking Jews of Alexandria, the Greek ángelos (άγγελος: "messenger") translates the Hebrew word mal'ak, while daimon (or neuter daimonion) carries the meaning of a natural spirit that is less than divine (see supernatural) and translates the Hebrew words for idols, foreign gods, certain beasts, and natural evils. The usage of daimon in the New Testament's original Greek text, caused the Greek word to be applied to the Judeo-Christian concept of an evil spirit by the early 2nd century AD.
Satanists have used the word demon to define a knowledge that has been banned by the Church.
Wikipedia: Daemon (classical mythology)
Enoch 1 talks about the sons of God that mates with the daughters of man being the fallen host in hell. If you follow Revelations, the rebellious angels under Lucifer are still in Heaven awaiting Michael to release them for the war in Heaven to come to earth:
Satan means adversary in Hebrew and was either not the original name to the leader of the rebellious whether he be Lucifer or Sammael (who Rabbinic lore is the "Chief of Satans") or Satan is a title for a group of angels that leads the rebellious to fall. Let it be noted that Lucifer is included in Gustav Davidson's list of the fallen as #57 by alphabetical order though he was left out of the list posted a few posts before mine.
There are more then one fallen angel as Lucifer (the morning star) is a angel an he was the reason of the fallen because he wanted his own kindgom so therefore Jehovah banned him and any of the angels that agree with lucifer. He is the ruler of hell and it his job to test both humans and the fallen. Sammeal/Satan is the only archangel to fallen and he rules in hell as the prince. Ori was one Fallen it was his job to hell luicfer by killing any rouge demons. Also he was excellent at seducing both men and women. Gusion (fallen) was known for seeing the future, he was also Ori friend, it was said that he help Ori in battle against Sarteal. Sarteal (fallen) want to to rule hell instead of Lucifer.
Some of the fallen mated with humans and produced nephilim (half-angel half-human) There are seven archangels and they are 1. Uriel, one of the holy angels, who presides over clamer and terror 2. Raphael, one of the holy angels, who presides over the spirts of men 3. Raguel, one of the holy angels, who take vengeance on the world of the luminaries 4. Micheal, one of the holy angels, to wit, he that is set over the best part of mankind and chos 5. Sarakiel, one of the holy angels, who is set over the sports, who sin in the spirt (and the only female archangel) 6. Gabriel, one of the holy angels, who is over paradise and the serpents and the cherubim 7. Remiel, one of the holy Angels, whom god set over those who rise - the book of Enoch 20:1-8 Therefore Micheal can't be a fallen.
A-Z Guide of demons, devils, and Fallen Angels
Abbadona= a fallen angel, a seraph. Is called "the penitent angel" as he was not committed to the rebellion
Adremelec= (King of Fire) one of the throne angels. He is 8th of the 10 archdemons; a great minister and chancelor of the Order of the Fly; a Order founded by Beelzebub
Agares= one of the Order of Virtues, now a Duke in hell, servedby 31 legions of infernal spirits. Said to teach languages and cause earthquakes
Agniel= taught men the enchantment of roots and the secrets of conjury, as well as using these arts to seduce one of the daughters
Amezyarak= an angel who taught conjurers and root cutters their art. One of the original 200 watchers
Amy= one of the angel of the orders of angel and powers. Great President in hell. He "gives perfect knowledge of astrology and liberal arts"
Anmael= sometimes identified with Semyaza, for it makes a bargain with a mortal woman in connection with the revelation of god
Arakiel= (Araqiel) one of the watchers that taught human beings the signs of the earth; still said to lead souls to judgement
Araziel= one of the watchers "my moon is god"
Ariel= in cabala he is regarded as formally of the order of virtues. Was overcome on the first day of the war in heaven
Armaros= one of the watchers who taught "the resolving of enchantments"
Armen= one of the watchers
Asbeel= (deserter from god) He imparted to the holy sons of god evil counsel and led them astray through the daughters of man
Asmoday= a fallen angel who has wings and flies about, and knowledge of the future. Governs 72 legions of infernal spirits. Teaches mathematics and can make men invisible.
Asmodeus= (Creature of Judgment) He is a Persian rather than jewish demon. A raging fiend. Son of Lilith by Samael
Astaroth= one of the seraph, now a great Duke in hell. An ancient god of Syria. One of the & princes of hell to visit Faust
Astoreth= fallen angel, equal with Astarte
Atarculph= leader of fallen angels as listed in Enoch
Auza= fallen angel who had cardinal knowledge of the daughters of men
Azaradel= watcher who taught men the motions of the moon
Azazel= (Gods Strength) Chief of the 200 fallen angels. Taught men to fashion swords and shields. Women learned the art of beautifying eye-lids. Refused to bow before adam. Claiming "Why should a son of fire fall down before a son of clay." One possible origin for the Hanging Man in the Tarot deck
Azza= (the strong) Suspended between heaven and earth for fornicating with human women
Azzael= (Whom God Strengthens) taught witchcraft. Punished with Azza in the same manner. Succumbed to the flesh of Lemech's daughter Naamah. She gave birth to Azza.
Balam= formerly of the order of dominations. Now a terrible and powerful king in hell, commanding 40 legions of infernal spirits.
Baraqel= one of the watchers
Barbatos= formerly of the order of virtues. A great Duke commanding30 legions of spirits. Gives understanding of bird songs and sees future.
Barbiel= Once prince of the orders of virtue and archangels. Now is one of the 7 electors, under the suzerainty of Zaphiel
Batarjal= one of the watchers
Baraqijal= taught men astrology
Beelzebub= (God of Flies) chief of the 9 evil hierarchies of the underworld. Prince of devils. Next to Satan in power and crime.
Beliar= (Worthless) equal to Belial and to Satan. The ultimate evil
Busasejal= one of the watchers
Byleth= one of the order of powers. Rules 85 legions of demons
Caim= once the order of angels. Now a great President, commands 30 legions of demons
Carnivean= ex prince of the order of powers. Invoked in the litanies of the witches' sabbaths.
Carreau= ex-prince of the order of powers
Dagon= A fallen angel in Paradise Lost I
Danjal= one of the fallen angels according to Enoch. He exercises authority over lawyers
Exael= watcher who according to Enoch "taught men to fabricate engines of war, works in silver and gold, and uses of gems and perfumes
Ezeqeel= a fallen angel who taught "augury from the clouds" Meteorology
Flauros= a gread Duke commanding 36 legions of the damned. Gives true answers to the past and future
Gaap= once of the order of powers. Now a great President and mighty prince in hell. As king of the south he commands 66 legions of infernal spirits
Gadreel= (God is my helper) one of the fallen angels that taught men to be familiar with weapons of war (Lead Eve astray)
Hakael= a fallen angel
Hananel= one of the watchers
Harut= a fallen angel
Iblis= (Despair) equated with Azazel and Satan
Ielahiah= formerly of the order of virtues. Protects Magistrates and renders decisions in legal suites
Iuvart= Ex-prince of the order of angels now serving in hell
Jegon= (Inciter) ringleader of the fallen angels. He helped Asbeel lead the sons of god astray
Jetiel= one of the 200 watchers according to Enoch
Kasdeja= (Kasdaye) a fallen angel who teaches a variety of demonic practices, including abortion
Kashdejan= taught men cures for various diseases, including those of the mind.
Kakabel= taught astrology and the science of the constellations
Kawkabel= (Kokbiel) a fallen angel commanding 365,000 spirits. Instructs his fellows in astrology
Lau(V)iah=once of the orders of thrones and cherubim
Leviathan=another name for Tiamat. Demon from the sea according to the bible. Name translates in hebrew to "that which gathers itself together in folds" Believed to be a female sea-dragon
Mammon= (riches) a fallen angel now ruling in hell as one of the archdemons and prince of tempters
Marchosias= one of the orders of dominations. In hell he is a mighty marquis.
Mephistopheles= (he who loves not the light) a fallen archangel, one of the 7 great princes of hell
Meresin= a fallen angel, Chief of the Ariel powers. Lord of thunder and lightning in hell
Moloc(h)= fallen angel. Described as "the fiercest spirit/ that fought in the heavens; now fiercer by despair. A Canaanitish god of fire whom children were sacrificed
Mulciber= once built in heaven high towers. Now fallen
Murmur= once of the orders of thrones and angels. Now a great Duke commanding 30 legions of the damned
Nelchael= once belonging to the order of thrones and one of the 72 angels bearing the mystical name of god. In hell he teaches astronomy, math, and geography to his fellow demons
Nilaihah= once of the order of dominations
Oeillet= once of the order of dominations
Olivier=ex-prince of the order of archangels
Pharmoros= taught pharmacy, herbal lore, practial medicine and diagnosis of illness
Paimon= (tinkling sound)nonce of the order of dominations. In hell a great king, obedient only to Lucifer. Commands 200 legions of spirits
Penemue= (the inside) the fallen angel who taught mankind how to write with ink and paper. He also taught the children of men the bitter and the sweet and the secrets of their wisdom
Procell= once of the order of powers. Now a great Duke commanding 48 legions of infernal spirits. Teaches geometry and liberal arts.
Pursan= once of the orders of virtues and thrones. Now a king commanding 22 legions of infernal spirits
Qenna - Egyptian mythology - was the name of a merchant in Ancient Egypt, in whose tomb was found the Papyrus of Qenna, a part of the Book of the Dead.
Raum= once of the order of thrones. Now a great Earl commanding 30 legions of infernal spirits
Rimmon= (roarer, exalted) a fallen archangel. Demon of storms
Rosier= once of the order of dominations. Now fallen.
Rumael= fallen angel that requires all the deceased to write down all evil deeds and passes judgement
Samael= (Poison Angel) equated with Satan, Lucifer and the angel of death. Cohort of Lilith. Once of the order of Seraphim. Prince of demons and magician. In hell he commands 2 million angels. Youngest and most virile of the 72 princes of hell.
Samsaweel= one of the watchers
Saraknyal= one of the watchers
Satan= in hebrew translates to adversary. First to fall.
Satanil= in Enoch II satan is referred to as this. (Great Prince of the Grigori)
Semyaza= one of the angels that fell to consort with women. Formally of the order of Serphim.
Senciner= Formally of the order of powers
Shamahiel= fallen angel who taught the signs of the sun
Sonneillon= Formally of the order of thrones
Talmaiel= descendant that escaped the flood and swords of avenging angels
Thammuz= Fallen angel in Milton's Paradise Lost
Tamiel= (Perfection of God)
Tumael= one of the watchers
Turel= one of the watchers
Urakabarameel= one of the leaders of the fallen angels
Verrier= once of the order of principalities
Verrine= once of the order of thrones
Vaul= (Uvall) formally of the order of powers. Now a great Duke with 37 legions of infernal spirits
Yomyael= one of the angels that fell with Satan
Zavebe= one of the watchers
Annestia = A fallen angel, often humans have been telling stories about her, known as a Goddess, roams around earth tempting weak souls, condemning them to hell.