E. De Felice and Surnames in Italy differ on the origin of the surname.

De Felice considers the etymology uncertain and puts forward several hypotheses. He considers a derivation from the Latin agaso ("stable boy, keeper of horses") improbable, as it has not continued in Neo-Latin except in Sardinian.

De Felice notes as possible derivations: a Late Latin personal name Agathius, masculine of Agatha; the Germanic personal name Agathio; or the old and dialectal names agasa, agassa and aiàssa ("magpie"), through an original nickname given to a person as talkative and cheeky as a magpie. He documents the name Agacia (pronounced agàzza) in Genoa in 1157, and notes that in France the surnames Agace and Agasse are attested in 1292, from the French agace or the Provençal agasa ("magpie"), of Germanic origin.

De Felice adds that the surname is widespread in northern Italy, as far as Tuscany, most frequently in Lombardy.

It is considered, on the other hand, to be a widespread toponymic surname, derived from Medieval Latin ad gagium ("next to the wood"), where gagium is a microtoponym and comes from the Lombard gahagi ("forbidden forest").