We have talked about the name of the Angel of death, and I told my friend that there is no Angel called Izrael. Please, explain to us this point.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Allah has allotted the responsibility of taking out souls, of causing death, to the Angel of Death. There is nothing in Sharia that proves that his name is Azra-el. In fact, all that was mentioned in this respect was taken from Jewish books and we are ordered by the Messenger of Allah not to believe or disbelieve in the things they claim.
Allah knows best.