The authors agree that the surname has an origin linked to Greek, although with nuances according to the region considered. G. Rohlfs describes it as a surname of Greek-Byzantine origin, present in the province of Catanzaro —with records in Dinami, Girifalco and the Soverato area— and also in the region of Campania. He considers it a variant of Fagà, derived from the Greek φαγᾶς, meaning "the one who eats a lot".

E. Rossoni presents several hypotheses on the relation between Faga and Fagà. According to one of them, Faga would be native to Piedmont and would have given rise, on moving to Calabria in the 13th century, to the rarer form Fagà. According to another, both forms would be autochthonous of Calabria and would derive from a nickname related to the proximity to a beech grove. A third hypothesis, which Rossoni presents as complementary, maintains that Fagà would have been formed within the Greek dialects of the south from the term faghas, meaning "glutton" or "greedy eater", a word that is preserved in modern Greek. This interpretation does not exclude, according to the author, that the Faga families of Calabria have remote Piedmontese origins.

V. Blunda provides a perspective from Sicily: he relates the surname with the Greek phagàs, "glutton", and notes that the form would have arisen as a nickname applied to an ancestor for his great appetite, following the habitual patterns of the Sicilian nicknames of Greek origin derived from traits of conduct in popular tradition.