Müzeyyen
Yes. Müzeyyen comes via Turkish from Arabic root z-y-n (زين), specifically from words like muzayyan/muzīn meaning 'adorned' or 'made beautiful'.
Müzeyyen is uncommon in most Arabic-speaking countries but has real historical usage in Turkey and among Turkish-speaking Muslim communities; overall it is relatively rare internationally.
Yes. Common Latin-script transliterations include Muzeyyen or Muzayyen; the Turkish orthography uses 'ü' to reflect vowel quality.
The name carries aesthetic meaning ('adorned') rather than a specific theological or legal sense. It is culturally acceptable as a Muslim feminine name because it derives from Arabic vocabulary with neutral/positive meaning.
The Arabic lexical pattern yields masculine forms like Muzayyan (مُزَيَّن) as descriptive epithets; however, Müzeyyen is specifically feminine in Turkish usage.