Is there a Christian name of the Destroyer Angel?
No Christian Traditions have a Christian name for the Destroyer Angel named such in the texts of Sacred Scriptures.
The destroying angel is also commonly referred to as the angel of death. On numerous occasions, God used angelic beings— heavenly messengers of some kind—to bring judgment to sinners on earth. Various Bible translations refer to this being as a “destroying angel.” There is no clear biblical evidence that any one particular angel was given the title “destroying angel” or “angel of death.” The most we can say is that the Bible’s mentions of a “destroying angel” are references to a heavenly being or beings that came to destroy those under God’s judgment.
The destroying angel or angel of death in the Hebrew Bible is an entity sent out by Yahweh on several occasions to kill enemies of the Israelites. In 2 Samuel 24:15, he kills the inhabitants of Jerusalem. In I Chronicles 21:15, the same "angel of the Lord" is seen by David to stand "between the earth and the heaven, with a drawn sword in his hand stretched out against Jerusalem." Later, in II Kings 19:35, the angel kills 185,000 men of Sennacherib's Assyrian army, thereby saving Hezekiah's Jerusalem.
The angel (malak) is referred to under various terms, including Mashḥit, meaning "destroyer" (pron. mash-heet(h) or -kheet(h)) (Mashchit(h), מַשְׁחִית and Ha-Mashchit(h)/Ha-Mashḥit, הַמַשְׁחִית), "destroying angel" (מַלְאָך הַמַשְׁחִית, malak ha-mashḥit or in the plural מַשְׁחִיתִים, mashchitim/mashchithim/mashḥitim—"spoilers, ravagers"), Angel of the Lord, (מְמִיתִים, memitim—"executioners", "slayers") is found in Job 33:22 and in Proverbs 16:14 in the plural, "Messengers of death". - Destroying angel (Wikipedia)
Of all names given to angels in God’s service, only three are found in Scriptures: Michael, Raphael and Gabriel.
In fact it is tradition, in the Catholic Church not to give names to angels.
The practice of assigning names to the Holy Angels should be discouraged, except in the cases of Gabriel, Raphael and Michael whose names are contained in Holy Scripture. - Directory on Popular Piety and the Liturgy (217)
The thought of an angel that brings death is an ominous one indeed, and it's small wonder such a figure might be associated with an evil nature given many people's fears about what happens after life ends. This has led some people to a belief that there is a close link between the death angel and the figure of Satan. However, there is no Christian biblical reference that Satan and this figure are one and the same. Rather, the Angel of Death is portrayed as someone doing God's work to help people as they reach fated end of their lives.
Allegorical skeletal representation of the Angel of Death (created in the XVII. century) in the church of San Pietro in Vincoli
The Nazi Josef Mengele (16 March 1911 – 7 February 1979), a German Schutzstaffel (SS) officer and physician in Auschwitz concentration camp during World War II was also known as the Angel of Death.