Qaisar
No; 'Qaisar' (Caesar) is not a Quranic name. It is an historical title referenced in Islamic historiography, not a Quranic personal name.
The term originates from Latin 'Caesar' and entered Persian and Arabic as a title; later it was sometimes used as a personal name in Persianate and South Asian cultures.
Historically it was used to refer to emperors (notably Byzantine rulers) in medieval Islamic chronicles and as an honorific borrowed into administrative and literary language.
Yes, many Muslim families, especially in Persianate or South Asian contexts, have historically used titles like Qaisar as names. It is culturally acceptable though not religiously prescribed.
Common transliterations include Qaisar, Qaiser, Qaysar, Kaisar, and the European 'Kaiser'.