Gökçe
Yes. Gökçe is of Turkish origin and has been used historically within Ottoman and Anatolian Turkic-speaking Muslim communities; it is a cultural rather than a Quranic name.
Gökçe evokes the sky—blue color, clarity, and poetic associations with the heavens; morphologically it is gök (sky) + -çe (a diminutive/adjectival suffix meaning 'like' or 'ish').
Pronounced roughly as GÖK-cheh; in English transcription often GOK-cheh, with the ö like the vowel in French 'bleu'.
Related masculine names include Gökhan and Gökay; the element gök appears in many Turkic male and female names.
Yes, provided families appreciate its Turkic cultural origin and phonology; it is not rooted in Arabic but is historically used within Muslim societies.