Mojgan
No. Mojgan is Persian in origin (مژگان) and later adopted into Turkish as Müjgan; its roots are in Persian vocabulary meaning 'eyelashes'.
Mojgan has historical attestation in Persian lexica and literary usage; it continues to appear in modern Iranian and Turkish naming practice, though it remains relatively uncommon.
In Persian poetic tradition eyelashes often symbolize delicate beauty, the power of a beloved's glance, and subtle grace; Mojgan evokes these poetic connotations.
In Turkish the name is commonly rendered and pronounced as Müjgan (MUEJ-gan), with the front rounded ü sound; in Persian it is pronounced MOZH-gān.
Yes. Mojgan is a culturally Persian/Turkish name without specific religious prohibitions and is used by Muslim families in relevant cultural regions; it is a literary, non-theophoric given name.