The authors propose very different origins for the surname Baffa.

E. Rossoni considers as the most likely hypothesis that it is a surname of Greek-Albanian origin, derived from the name of the city of Paphos, on the island of Cyprus, which arrived in Italy in the 15th century during the wars of the Turks against the Greek lands and the Republic of Venice. In some cases it could also be a variation of the surname Baffi.

V. Blunda presents it as a Sicilian surname of dialectal origin, formed from a pejorative nickname applied to women. He derives it from the dialectal expression cucuzza bàffa, meaning "a fat and slovenly woman", literally "flabby pumpkin". He recalls that nicknames based on vegetable metaphors to describe the female body in a mocking way were common in Sicilian rural culture, and reflect the crude language of the island's popular speech in the formation of hereditary surnames.