Ajwa
No. 'Ajwa' as a proper name or place is not in the Quran; the word itself is classical Arabic for a variety of date and is mentioned in hadith and pre-modern literature rather than the Quran.
Yes. The word 'Ajwa' appears in Islamic hadith literature and classical Arabic sources as the name of a variety of date associated with Medina; that cultural and textual presence is why it is used as a feminine given name.
Yes. Ajwa is a permissible Arabic name with neutral religious connotations; it denotes a fruit and the associated positive qualities of sweetness and blessing.
Relatively uncommon. Ajwa is used in some Arab and Muslim communities but remains rare compared with more widely used Arabic feminine names.
Common transliterations include Ajwa and Ajwah; the Arabic spelling is عجوة and the initial consonant is the letter ʿayn (ʿ).