The name of Jibril (also know as "Gabriel" in English) and Mika'il are indeed written in Quran. But the names of Azrael and Israfil are not. How do we know actual names of these angels? Did we Muslims imported angel names from other religions?
2 Answers
Izra'il:
There is no mention tying that name to the angel of death in either Quran or saheeh Hadiths. The name Azrael comes from Jewish traditions incorporated later by some scholars as part of what is known as "Isra'eliat".
Mika'il
He is mentioned in the Quran as Mikal ميكال.
Whoever is an enemy to Allah and His angels and His messengers and Gabriel and Michael - then indeed, Allah is an enemy to the disbelievers.
The spelling Mika'il ميكائيل comes from a few disputed Hadith (see below) and Jewish traditions.
Israfil
This name has only been mentioned in a few Hadiths such as this one:
أَخْبَرَنَا أَحْمَدُ بْنُ حَفْصٍ قَالَ حَدَّثَنِي أَبِي قَالَ حَدَّثَنِي إِبْرَاهِيمُ عَنْ سُفْيَانَ بْنِ سَعِيدٍ عَنْ أَبِي حَسَّانَ عَنْ جَسْرَةَ عَنْ عَائِشَةَ أَنَّهَا قَالَتْ قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ اللَّهُمَّ رَبَّ جِبْرَائِيلَ وَمِيكَائِيلَ وَرَبَّ إِسْرَافِيلَ أَعُوذُ بِكَ مِنْ حَرِّ النَّارِ وَمِنْ عَذَابِ الْقَبْرِ
"Oh Allah, god of Jibreel and Mika'il and god of Israfil. I seek your refuge from hellfire".
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4I must disagree: The spelling Mika'il ميكائيل is an approved qiraa'a approved by the quraa' Nafi', ibn Kathir, ibn 'Amir, Hamzah, al-Kissaa-i , Abu Ja'afar and Khalaf and it is also the riwaya of Shoaba 'an 'Asim. So the exception of this is ميكال which is only the riwaya of Hafs 'an 'Asim and of the both Basri quraa' Ya'qub and abu 'Amr.– Medi1Saif ♦Commented Jun 8, 2016 at 10:44
Gabriel is named in the Quran in 2:97, 2:98 and 66:4.
The following Qirat are mentioned in Tafsir Qurtubi:
جِبْرِيلٌ
جَبْرِيل
جَبْرَئِيل
جَبْرِئل
جبرائل
جبرئييل
Michael is named in the Quran in 2:98.
The Qirat mentioned in Tafsir Qurtubi include:
ميكاييل
ميكائيل
ميكال
ميكئيل
ميكاييل
ميكاءل
Israfil is named with the above two in Sahih Hadith:
قَالَ سَأَلْتُ عَائِشَةَ أُمَّ الْمُؤْمِنِينَ بِأَىِّ شَىْءٍ كَانَ نَبِيُّ اللَّهِ صلى الله عليه وسلم يَفْتَتِحُ صَلاَتَهُ إِذَا قَامَ مِنَ اللَّيْلِ قَالَتْ كَانَ إِذَا قَامَ مِنَ اللَّيْلِ افْتَتَحَ صَلاَتَهُ " اللَّهُمَّ رَبَّ جِبْرَائِيلَ وَمِيكَائِيلَ وَإِسْرَافِيلَ فَاطِرَ السَّمَوَاتِ وَالأَرْضِ عَالِمَ الْغَيْبِ وَالشَّهَادَةِ أَنْتَ تَحْكُمُ بَيْنَ عِبَادِكَ فِيمَا كَانُوا فِيهِ يَخْتَلِفُونَ اهْدِنِي لِمَا اخْتُلِفَ فِيهِ مِنَ الْحَقِّ بِإِذْنِكَ إِنَّكَ تَهْدِي مَنْ تَشَاءُ إِلَى صِرَاطٍ مُسْتَقِيمٍ
I asked 'A'isha, the mother of the believers, (to tell me) the words with which the Messenger of Allah (ﷺ) commenced the prayer when he got up at night.
She said: When he got up at night he would commence his prayer with these words:
O Allah, Lord of Gabriel, and Michael, and Israfil, the Creator of the heavens and the earth, Who knowest the unseen and the seen; Thou decidest amongst Thy servants concerning their differences. Guide me with Thy permission in the divergent views (which the people) hold about Truth, for it is Thou Who guidest whom Thou wilt to the Straight Path.
Azrael ( عزرائيل ) is not named in the Quran nor in authentic Hadith. The title mentioned in the Quran in 32:11 is ملك الموت lit. Angel of Death, and several hadith and other reports name the angels the angels as 'Gabriel, Michael, Israfil and ملك الموت', not using the name Azrael . The name is mentioned in some athar and some tafsirs mention it such as Qurtubi and Razi etc. however there is no consensus about its authenticity and many scholars doubt it.