The authors agree that the surname was formed from the personal name Anfosso or Anfussus, an archaic form of the name Alfonso.

E. De Felice specifies that the name Anfosso or Anfusso is documented as early as the 12th and 13th centuries in Liguria and Piedmont as Anfossus and Anfussus, and in Provence —probably the centre of radiation in Italy— as Anfos, Anfous and Amphoux. He adds that there is a second variant: one of the many regional or dialectal forms that the name Alfonso takes in the Naples area and in other southern zones.

De Felice notes that the surname is widespread, in the An- forms, from Liguria to Piedmont and also Lombardy; while it is peculiar to the south —especially the Naples area and Sicily— for the forms Affuso and Alfuso, and in part also Anfus(s)o.

E. Rossoni agrees on the derivation from the medieval name Anfossus. He documents it in the Diplomatic Code of Medieval Lombardy in 1179, and adds that it appears in Pisa in the 12th century. He notes that the family of notaries Anfossi is documented in Taggia in the 17th century.