The authors agree in noting a Greek origin for this surname, although they differ on what the exact root would be. G. Rohlfs and F. Miranda converge in deriving it from the Greek κουρούπης, meaning "shaven" or "with cropped hair", interpreting it as a descriptive nickname referring to the appearance of the first bearer. V. Blunda agrees with this line in noting the form coyroýpes with the same sense of "shaven, shorn", and highlights that the nickname could have been motivated by the baldness or the close-cropped haircut of an ancestor.

Miranda adds a second independent etymological hypothesis: the Sicilian word crupu, which designates a "land fertilised with much manure to make it a seedbed", in turn derived from the Greek χόπρος ("excrement"). According to this interpretation, the surname would have alluded to the trade of the one who used manure to cultivate the land. For his part, P. Durante proposes different Greek roots: krypto ("hidden") or krupala ("sandals"), without developing the link with the surname.

As for the geographical distribution, Rohlfs places the surname mainly in Calabria, in the zone of the Aspromonte and in the province of Catanzaro, noting also its presence in Sicily and its condition as a surname of Greek-Byzantine origin. Miranda specifies the Sicilian distribution in greater detail: he documents it in zones of Messina, Catania, Enna, Palermo, Syracuse and Trapani, as well as in the zone of the Strait and in the provinces of Reggio Calabria and Vibo Valentia. Outside southern Italy, Miranda mentions its presence in Lombardy, Lazio, Piedmont, Liguria, Tuscany and Puglia.