The authors agree that this surname has its roots in the Arabic term al-wazīr, related to positions of authority or judicial and policing functions. E. De Felice details that the base is the nickname and later personal name agozzino, formed from the occupational term agozzino —in old Sicilian algoziru—, an adaptation of the Arabic al-wazīr, with the sense of "official of judicial and policing bodies" and later "prison overseer or guard". De Felice notes that the Catalan algozir and algutzir and the Spanish alguacil contributed to the spread of the term, and that the name is documented in Genoa as early as the 12th century in Latinised forms such as Agozinus, Aguzinus and Aguxinus.

F. Miranda considers that Agozzino is a variant derived by transcription error from Algozzino, a typically Sicilian surname, and specifies that in Sicily it is recorded in the provinces of Palermo, Agrigento, Messina, Syracuse, Enna, Trapani and Caltanissetta. Miranda interprets the Arabism with the sense of "minister, high official", in allusion to a first bearer who would have held positions of that kind. De Felice, for his part, locates the surname mainly in Liguria, the Campania region and Sicily.