Türkan
No. Türkan is a Turkish (Turkic/Ottoman) name with cultural and ethnic connotations; it is not mentioned in the Qur'an but is historically attested in Ottoman and modern Turkish usage.
Yes. The name has been borne by modern Turkish public figures; most famously the film star Türkan Şoray, confirming its real-world attestation in 20th-century Turkey.
In Turkish, the name is pronounced approximately [tyɾˈkan]; in English renderings it may appear as TUR-kan or TYUR-kahn.
Yes, if the family appreciates Turkic cultural heritage. It is not religiously specific and does not contravene Islamic naming norms, but its ethnic resonance is strongly Turkish.
Common Romanizations include Turkan (without diacritic) and Türkan (with the Turkish ü); these reflect the same name.