E. Rossoni proposes that this surname derives from the reduction of the initial syllable of given names such as Amerigo, Federigo, Oderigo or others similar, including their feminine variants. According to Rossoni, the surname is documented in different areas of Italy: in the province of Udine and its surroundings, in Rome, in Abruzzo —specifically in Montesilvano, in the Pescara area, and in L'Aquila—, and predominantly in Calabria, where it appears in Crotone and in the Catanzaro, Cosenza and Vibo Valentia areas, as well as in the province of Catania. This author also notes related variants: Righi, diffused throughout the centre-north of Italy, and Rigo, typical of the north-east of Italy, in the regions of Veneto, Friuli-Venezia Giulia and Trentino-Alto Adige.

G. Rohlfs proposes a different origin, not compatible with the previous one: for him, the surname is of Greek-Byzantine root and derives from the term of the Grecanic dialect of the Bova area riga, in turn from the Late Greek ρήγας, with the meaning of "king." Rohlfs documents its presence in Catanzaro, Cosenza and Reggio Calabria, as well as in localities of their respective provinces —Mangone, Paola, Briàtico, Sersale— and also in Basilicata. He further notes that in Greece the form Rigas survives as a surname, and refers the reader to the entry Righi.

Both proposals are independent of each other and cannot be reconciled: while Rossoni links the surname to the apocope of medieval anthroponyms, Rohlfs inscribes it in the Greek-Byzantine linguistic heritage of the far south of Italy.