Name of the Angel of Death: Is It ‘Azrael?
Question

Is there any evidence to show that the name of the Angel of Death is ‘Azrail (Azrael)?
Praise be to Allah.Name of the Angel of death
It is widely assumed that the name of the Angel of Death is ‘Azrail (Azrael), but there is nothing in the Quran or saheeh sunnah (authentic teachings) of the Prophet (peace and blessings of Allah be upon him) to indicate that this is his name. Rather this is narrated in some reports which may be from among the Israiliyyat (reports from Jewish sources). 
Based on this, we cannot be certain whether this is his name or not. So we cannot affirm that the name of the Angel of Death is ‘Azrail, nor can we deny it. Rather we should refer this matter to Allah and call him as Allah calls him, the ‘Angel of Death’. Allah says (interpretation of the meaning): 
“Say: The angel of death, who is set over you, will take your souls. Then you shall be brought to your Lord.” [Al-Sajdah 32:11] 
The name of the Angel of Death is not given in the Quran or in the saheeh ahadeeth (reports). His name is mentioned in some reports as ‘Azrail, but Allah knows best. 
Scholarly Views on the name of the Angel of Death
Al-Sindi said: “There is no marfoo’ hadeeth [one that can be traced back to the Prophet (peace and blessings of Allah be upon him)] which mentions his name.”
Al-Manawi said in Fayd al-Qadeer, after stating that the Angel of Death is known by the name ‘Azrail: “I have never seen any report giving his name as such.”
Shaykh al-Albani said in his comment on the words of al-Tahawi, “We believe in the Angel of Death who is appointed to take the souls of all creatures”: 
“This (the Angel of Death) is what he is called in the Quran. With regard to the name ‘Azrail which is widely known among the people, there is no basis for this, rather it comes from the Israiliyyat.” 
Shaykh Ibn ‘Uthaymeen said: 
“The Angel of Death” is well known by the name Azra’il, but this is not correct, rather this was narrated from Jewish sources. So we should not believe in this name, and we should call the one who is appointed over death “the Angel of Death,” as Allah called him in the verse (interpretation of the meaning): 
“Say: The angel of death, who is set over you, will take your souls. Then you shall be brought to your Lord.” [Al-Sajdah 32:11] (Fatawa Ibn ‘Uthaymeen)
Learn more about Angels in Islam in these answers: 843 , 9477 , and 96306 .
And Allah knows best.