What explanations have been offered for why Jesus never addressed God in His prayers by the name "Jehovah" or "Yahweh"?
In Aramaic, Jesus Christ addresses God as MarYA. In Aramaic Peshitta (Aramaic NT), you will see Jesus Christ saying MarYA several times.
"YA" (Yodh Alap) is Aramaic form of Hebrew "YH" in "YHWH." MarYA means "Master YA" in English. Aramaic was the spoken language of first century Israel. So they used MarYA to address God. So the names will also get changed when they are converted from Hebrew into Aramaic.
Here are some examples. I will put Hebrew on the left, Aramaic in the middle, and English on the right.
YH (Hebrew) - YA (Aramaic) - English
Yehochanan - Yochanan - John
Yehonathan - Yonathan - Jonathan
Yehoseph - Yoseph - Joseph
Yehoyachim - Yoyakim - Joachim
Aramaic was the spoken language of Jews in first century AD and upto 130 AD in second century AD.
From 131 AD, Jewish opposition started against Emperor Hadrian which led to the rise of Simon Bar Kokhba (also known as Simon Bar Kosiba) and Bar Kokhba revolt (132-135 AD). Simon Bar Kokhba revived Hebrew and tried to make Hebrew the official language of the state during Bar Kokhba revolt (132-135 AD) instead of Aramaic.
According to Dead Sea Scrolls archaeologist, Yigael Yadin, Aramaic was the spoken language of Jews until Simon bar Kokhba tried to restore Hebrew as the official language of Jews during Bar Kokhba revolt (132–135). Yigael Yadin noticed the shift from Aramaic to Hebrew during the time of Bar Kokhba revolt—in his book Bar Kokhba: The Rediscovery of the Legendary Hero of the Last Jewish Revolt Against Imperial Rome, Yadin notes, "It is interesting that the earlier documents are written in Aramaic while the later ones are in Hebrew. Possibly the change was made by a special decree of Bar-Kokhba who wanted to restore Hebrew as the official language of the state" (page 181).
In Book "A Roadmap to the Heavens: An Anthropological Study of Hegemony among Priests, Sages, and Laymen (Judaism and Jewish Life)" by Sigalit Ben-Zion (Page 155), Yadin remarked: "it seems that this change came as a result of the order that was given by Bar Kokhba, who wanted to revive the Hebrew language and make it the official language of the state."
The names also "started" to convert back to Hebrew during Bar Kokhba revolt (132-135 AD). From this point onwards, Hebrew "YH" was used instead of Aramaic "YA."
For Example, Yoseph Bar Yoseph in Aramaic became Yehoseph Ben Yehoseph in Hebrew during Bar Kokhba revolt (132-135 AD).
As you know, Aramaic word "Bar" means son ("Bar"tholomew, "Bar"abbas, "Bar"nabbas, "Bar"sabbas, etc) while the word for son in Hebrew is Ben.
Here is the link where you can see Yehoseph Ben Yehoseph in Bar Kokhba letters.
The word Jehovah is a Latin version of the Tetragrammaton, usually considered the Hebrew name of God. Most scholars consider Jehovah "a hybrid form derived by combining the Latin letters JHVH with the vowels of Adonai", and not to have been used before 1100AD. Obviously Jesus would not have used a word invented 1100 years after his earthly life.
It is widely thought that Jesus DID use the Hebrew name of God, in John 8:58:
“Very truly I tell you,” Jesus answered, “before Abraham was born, I am!”
The reaction of the hearers was such that they clearly believed he was using the name of God.
It was the practice of the Jews not to use the name of God at that time, so he may simply have wished to not muddy the waters by giving offence. Technically the name YHWH applies just as much to him as it does the Father, so that may have accounted for it.
If Jehovah were an exclusive name for God the Father, then it would be appropriate for Jesus to have used that name, along with a myriad of other names (Jehova-Jireh, El Shaddai, etc.).
However, if the name "Jehovah" applied to the Trinity, then it would seem odd for Jesus to refer to the Father with a term that also referred to Himself as part of the Trinity.
Jesus most often uses "Father" when addressing the Father, which is a relational term.
At that time Jesus declared, “I thank you, Father, Lord of heaven and earth, that you have hidden these things from the wise and understanding and revealed them to little children; yes, Father, for such was your gracious will. Matthew 11:25-26 ESV
And going a little farther he fell on his face and prayed, saying, “My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as you will.” Matthew 26:39 ESV
Then Jesus, calling out with a loud voice, said, “Father, into your hands I commit my spirit!” And having said this he breathed his last. Luke 23:46 ESV
When Jesus had spoken these words, he lifted up his eyes to heaven, and said, “Father, the hour has come; glorify your Son that the Son may glorify you. John 17:1 ESV
And now, Father, glorify me in your own presence with the glory that I had with you before the world existed. John 17:5 ESV
And I am no longer in the world, but they are in the world, and I am coming to you. Holy Father, keep them in your name, which you have given me, that they may be one, even as we are one. John 17:11 ESV
Father, I desire that they also, whom you have given me, may be with me where I am, to see my glory that you have given me because you loved me before the foundation of the world. John 17:24 ESV
O righteous Father, even though the world does not know you, I know you, and these know that you have sent me. John 17:25 ESV
Actually he did use it. in Luke 4:17-19 in the 19th verse the name Jehovah is used. Jesus most definitely used his fathers name while reading aloud the scroll, contrary from the scribes and pharisees who he called "offspring of vipers". and in fact while there are countless titles for God. The bible teaches that he has a personal name.
Yes a personal name. That name is Jehovah. If you look at Psalms 83:18 it says "You whose NAME is Jehovah, you alone are the most high over all the earth." In fact the divine name actually appears upwards of 6,000 times in the hebrew scriptures alone.
No doubt you have noticed the word LORD capitalized as such. That capitalization indicates the word Lord or "Adonai" has been subsituted for the divine name. (In contrast to simply lord) I promise you this, check in the beginning of your bible in the letter from the translation committee. They might even use the Hebrew transliteration in their explanation "YAWHH" The translation committee did this in adherence to the Jewish religous leader's tradition not to say the name.The same ones known by Jesus as "Hypocrites" and "offspring of Vipers."
However Jesus himself said he has made God's name known to them. (john 17:26) Moreover he also prayed for the sanctification of that name. At (Matthew 6:9) we read "Our father in heaven let your name be sanctified" or in some translations "hallowed by thy name." Either way Jesus himself did pray for God's name Jehovah to be honoured and glorified. Whats more he gave it prime importance by stating it first. I myself have just happily carried on the work and the honour of making the greatest name ever known to all who read. Jehovah which litterally means: He causes to become. For more information about the name and who today is carrying on Jesus's work of sanctifying the name please see Jw.org
Since Jesus was the Father's Son, it's not likely he would refer to Him by the Tetragrammaton יהוה. I don't call my father by his first name, because it's considered disrespectful. Even then, children would call their father and mother as אבא and אמא, respectfully.
Since the NT comes to us in Greek, we can't really say for sure that Jesus did not sometimes use the Tetragrammaton (when referring to the Father in an impersonal way to others). The Tetragrammaton יהוה is a Hebrew word, so why should one expect to find it in Greek scriptures? Do we find it in the LXX? No. We find κυριος instead.
To answer this question we must recall two statements by Jesus in his High Priestly Prayer:
"I revealed your Name to the men whom You have given Me out of the world." (Jn 17:6)
"And I made known to them your Name, and will make it known, so that the Love with which You loved Me may be in them, and I in them." (Jn 17:26)
Now, in what sense did Jesus perform a fuller revelation of the divine Name already revealed to Moses in the burning bush?
To answer that, let's recall that the name YHWH, if vocalized YaHWeH, is hifil stem, third person, singular, imperfect form, of the verb "hwh", an earlier variant of the root "hyh", "to be", meaning "He causes to be". Thus, while the Name of Ex 3:14, "I Am", denotes God as He Is in Himself - Absolute, Subsistent Being -, the Name in Ex 3:15, which was the one used by the Israelites, denotes God as viewed by creatures: He who causes them to be.
The problem here is that causing creatures to be is not something that God does by necessity of nature, but something that He freely decided to do. For Catholics, this notion was defined in the strongest terms by the Ecumenical Council Vatican I, Constitution "Dei Filius", Chapter 1 "Of God, the Creator of all Things", canon 5:
If any one [...] shall say that God created, not by his will, free from all necessity, but by a necessity equal to the necessity whereby He loves Himself [...]: let him be anathema.
Since causing creatures to be is not something that God does by necessity of nature, but something that He freely decided to do, it seems that the name YaHWeH does not express the essence of God in Himself, but only his role from the viewpoint of creatures consequent to his free decision to create them. Since we exist precisely because of that free decision, YaHWeH expresses Who God is for us: He who causes us to be, whereas the essence of God in Himself would be expressed only by the Name in the first person revealed in Ex 3:14: Ehyeh, "I Am", or by its correspondent form when pronounced by a creature in the third person, which is the Name revealed in Ex 3:15 vocalized in qal stem: YiHWeH, "He Is", or more completely, "He Was, Is and Will Be".
Now, given that available evidence, e.g. Hebrew teophoric names, points to ancient Israelites pronouncing the Tetragrammaton as YaHWeH, is there a sense in which YaHWeH expresses the essence of God in Himself? Indeed there is, and we came to know it precisely from Jesus' revelation that God eternally begets a consubstantial Son. Now, this eternal generation is not by contingent free will but by nature:
"The Father begot the Son, not by will, nor by necessity, but by nature."
From the formula called the "Faith of Damasus" [Of uncertain author from Gaul about 500], Dz 15.
"Also, this Son is Son of God by nature, not by adoption, Whom we must believe God the Father begot neither by will nor by necessity; for, neither does any necessity happen [al. capit, 'take hold'] in God, nor does will precede wisdom."
From the Creed of Faith of the Council of Toledo XI, 675, Dz 276.
Thus, there is a sense in which YaHWeH, "He causes to be", expresses the essence of God in Himself, and it is by changing the verb "to be" in the contingent sense by "to Be" in the subsistent sense: "He causes to Be", by nature, his consubstantial Son, and causes Him to Be the same reality as He Is, the only Subsistent Being, begetting Him in eternity, not creating Him.
Jesús, by revealing Himself as "I Am" (Jn 8:24,28,58; Jn 13:19), one with the Father (Jn 10:30), simultaneously reveals that God is not only "He causes to be" contingently ad extra, but also, and above all, "He causes to Be" (capitalized "Be" to denote Subsistent Being) esentially ad intra. The essence of God is not only "Being" but also "causing to Be", begetting his consubstantial Son. Thus, "Father" from the viewpoint of Jesus, and "God the Father" from our viewpoint, is the full sense of the name YaHWeH.
Did Miriam (Mary) call her son Jesus? Nope his name was 'yeshua ben yosef' (which in itself is just an approximation due to language and alphabet limitations). Similarly, Jesus would never address God by 'Jehovah'. However he could have addressed him as any of the names of God: Names of God in Judaism (Wikipedia).
The bible may have translated the name used to 'Jehovah' to remain consistent for the reader who may not understand the different names of God.
As a side note, my personal favorite is "El Roi" which sounds like "El Row He" or "Elroy" from The Jetsons: God Who Sees me (All seeing God, sometimes denoted by the eye of providence); Hagar's name for God when He saw her affliction (Gen. 16:13).
Or El Kanno which sounds like "El Can Know": The Jealous God (Exod. 20:5; 34:14; Num. 5:14, 30; Deut. 4:24; 5:9; 6:15; Jos. 24:19; 1 Ki. 19:10, 14; Ezek. 39:25; Joel 2:18; Nah. 1:2; Zech. 1:14; 8:2). Suggests that God watches us lovingly and closely, like a faithful and passionate bridegroom watches over his betrothed.