Al-Hayy – Al-Qayyūm
The Ever-Living – The All-Sustainer
The Ever-Living is the One Who has permanent life and existence that has no beginning or end; all life in existence stems from Him, Exalted be He.
This great name occurs 5 times in the Qur’an, most notably in the Verse of Al-Kursi: {Allah – there is no god except Him, the Ever-Living, the All-Sustainer.} [Sūrat Al-Baqarah: 255] Another verse reads, {And rely upon the Ever-Living who does not die, and exalt [Allah] with His praise. And sufficient is He to be All-Aware with the sins of His servants.} [Sūrat Al-Furqān: 58] And it occurs in the Sunnah in the Prophet’s supplication, “O Allah, the Ever-Living, the All-Sustainer, I seek relief in Your mercy.”[1] And in the Hadīth in which Ibn ‘Abbās (may Allah be pleased with him) reported that the Prophet (may Allah’s peace and blessings be upon him) used to say, “O Allah, I surrender to You, I believe in You, I rely on You, I return in repentance to You, I take your opponents as enemies. I seek refuge with Your Honor, there is no god but You, that You do not lead me astray. You are the Ever-Living who never dies, yet the jinn and humans will all die.” [Narrated by Muslim]
Al-Qayyūm
As for the name ‘the All-Sustainer’
He is the All-Sustainer, the One Who does not need any of His creation; and He is sustaining all those in the heavens and earth who all stand in need of Him.
This noble name occurs 3 times in the Qur’an, most notably in the Verse of Al-Kursi: {Allah – there is no god except Him, the Ever-Living, the All-Sustainer.} [Sūrat Al-Baqarah: 255] And also in the initial verses in Sūrat Āl-‘Imrān: {Alif, Lam, Meem. Allah – there is no god except Him, the Ever-Living, the All-Sustainer.} [Sūrat Āl-‘Imrān: 1-2]In light of these two great names, I would say:
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[1] Narrated by Al-Tirmidhi
[2] Narrated by Al-Nasā’i