Gürkan
No. Gürkan is of Turkic/Mongolic historical origin and is not found in the Qur'an; it derives from a title used among Mongol and Timurid elites.
Guregen (also spelled gurkan) literally referred to a son-in-law of a khan, indicating dynastic alliance and elevated status.
Yes; it appears in Timurid and other Central Asian sources as an honorific and later transferred into personal and family names.
It exists today as a given name and surname in Turkey but remains relatively uncommon and regionally concentrated.
Not specifically; its significance is historical and genealogical rather than religious or scriptural.