The authors agree in pointing to a Greek origin for this surname, although they differ on the details. G. Rohlfs proposes two possible routes: that it comes from the place name Ascèa, a locality in the province of Salerno, or —more probably— from the Greek surname Ἀξιώτης, in relation to the Byzantine presence in southern Italy. He places the surname in the Reggio Calabria area.

E. Rossoni also links the surname to the gentilic derived from Ascea and notes that its distribution covers mainly the Reggio Calabria area, with the variant Asciuti documented in the Naples area.

V. Blunda offers a different reading: he derives it from the Greek Acsiòtes, meaning "native of Naxos", in reference to the island of Naxos, in the Cyclades archipelago. According to this interpretation, the surname would have originally functioned as a gentilic applied to an ancestor coming from that island. The variant Azoti would represent a graphic adaptation of the same etymon in other areas of Sicily.