Barbad
Yes. Barbad is attested in Persian historical and literary sources as the renowned Sassanian court musician; the name is historically documented rather than being a modern invention.
There is no single agreed lexical meaning; the name is Middle Persian in origin and is best known as the proper name of the musician rather than a transparent common-word meaning.
Yes, Barbad appears sporadically among Persian-speaking and culturally Persianate families who value classical Persian literature and history; it is rare but acceptable as a given name.
Barbad appears in Persian literary tradition and courtly chronicles; later poets and historians refer to him when describing Sassanian music and the cultural life of the royal court.
The historical and standard Persian spelling is باربد.