E. Rossoni notes that this surname is not very frequent and presents areas of presence in the provinces of Prato, Florence, Arezzo, Pesaro, Rimini, Perugia, Macerata, Ascoli Piceno and Rome. According to Rossoni, the surname would derive from the Latin name Coccius, the gentilic name of the Gens Cocceia, a family that had properties in central Italy and in the Benevento area. It is not ruled out that in some cases it may come from dialectal diminutive forms of the name Francesco. As an early historical testimony, Rossoni mentions the Venetian chronicler Marcus Antonius Coccius Sabellicus (1436–1506).

V. Blunda proposes, on the other hand, a different origin for the surname in Sicily: he links it to the dialectal word cociu, which means "grain, berry", a term that designated the cereal grain, the loose seed or the small fruit of the vine and the olive. As a surname, it could have arisen from a nickname applied to a person of short stature or slight build, or as a metonymic reference to the one who worked in the gathering and selection of grains. The surname therefore has independent origins in different regions of Italy.