Aybak
No. Aybak is of Turkic origin (ay = moon; bäk/beg = lord). It was used within Islamic societies—Persianate and Ottoman contexts—but its elements are Turkic rather than Arabic.
Yes. The form Aibak (often Latinized) appears in history: Qutb al-Din Aibak (d. 1210) was a Turkic Mamluk commander who became the first Sultan of the Delhi Sultanate; his name reflects Turkic naming elements used in Islamic polities.
No. The name does not occur in the Quran or canonical Hadith collections; its attestation is in historical chronicles and inscriptions from Turkic-Islamic contexts.
Yes. Aybak has historical Islamic usage and a clear meaning; families often choose it for its poetic 'moon' imagery and historical resonance, particularly in Turkic cultural spheres.
Common renderings are ايبك / أيبك in Arabic script or ایبک in Urdu, but native Turkish orthography is Aybak. Meanings are typically supplied in the target language (e.g., 'سيد القمر' or 'چاند کا سردار').