The Bible gives the names of two of God’s holy angels: Gabriel and Michael. We have no other names beyond those two. There is a man named Phanuel (Luke 2:36), but no angel named Phanuel in the Bible. We can attribute the idea that an angel named Phanuel exists to his mention in the apocryphal Book of Enoch.
A good portion of the Book of Enoch deals with angelology and demonology. According to the Book of Enoch, Phanuel is one of four angels who stand before the throne of God—the other three being Michael, Gabriel, and Raphael. Phanuel is “the fourth, who presides over repentance, and the hope of those who will inherit eternal life” (Enoch 40:9). He is also said to have the task of “expelling the impious angels and prohibiting them from entering into presence of the Lord of spirits” (Enoch 40:7).
The mythology goes on to name Phanuel as the ruler of the Ophanim, angels in the throne room of God who never sleep. And he is one of the angels involved in the judgment of the wicked angels: “Phanuel shall be strengthened in that day and shall then cast [the demons] into a furnace of blazing fire, that the Lord of spirits may be avenged of them for their crimes; because they became ministers of Satan and seduced those who dwell upon earth” (Enoch 53:6).
The Bible does not give us much information about any of the angels, holy or otherwise. The Book of Enoch is a strange and sensationalistic work of non-canonical literature. We have no reason to accept the Book of Enoch as truth, with the exception of the portion of the Book of Enoch quoted in Jude 1:14–15. There’s no way to know if an angel named Phanuel actually exists, and investigations into mythology are ultimately unprofitable.