The authors agree that this surname derives from the familiar and affectionate name Rigo, an aphaeretic hypocoristic of Arrigo —that is, a form abbreviated by suppression of the initial syllable—, and also, in a non-relevant part, from other names ending in -rigo, such as Alderigo, Amerigo or Federigo. E. De Felice notes that the form Rigo prevails in the north-east of Italy, in the regions of Veneto, Friuli-Venezia Giulia and Trentino-Alto Adige, while Righetti and Righini are more frequent in Emilia-Romagna and Tuscany. Other variants such as Rigacci, Righeschi, Rigoli and Rigucci are of Tuscan distribution.

R. Brondolo explicitly links Arrigo with the Germanic name Enrico, and notes that from the same origin come related place names and surnames: Rigoli —documented in the Pisa area and the Como area—, Rigoni and Righini. He also mentions the form Rigaglia, which he interprets as "the children of an Enrico," with the accumulative suffix -aglia.

G. Rohlfs proposes a completely different etymology for the presence of this surname in southern Italy: he considers it of Greek-Byzantine origin, documented in the Cosenza area and also in Sicily. He interprets it as the old plural of Riga, derived from the Late Greek ρήγας ("king"), and links it to the Byzantine influence in the south of the Italian peninsula. This interpretation is independent and does not contradict the Germanic etymology, but points to a different geographic and historical origin for the southern forms of the surname.