The surname presents independent stems of origin (ceppi) with a presence in the Bari area and in the Palermo area as main nuclei, besides ramifications in Lombardy, Lazio, Piedmont, Tuscany, Veneto and Abruzzo. In Sicily it also appears in the Catania, Agrigento, Messina, Syracuse and Enna areas.

As for the origin, E. Rossoni and F. Miranda agree in pointing as a possible etymon to the Latin cognomen Genicus, of which Rossoni cites an epigraphic example: A. Genicus A. f. iter. duoviri locum dederunt. Miranda adds another Latin hypothesis: the contraction of the adjective geniculatus, in reference to the knee (geniculum), which would have become a byname and then a surname.

Miranda also considers a possible geographical origin, linked to the place name acqua di Genco, belonging to the municipality of Mezzojuso, in the Palermo area, or else to the genco variety of the almond tree, very widespread in the zones where the forms Genco and Genchi appear. For his part, Rossoni notes, following the linguist G. Rohlfs, that the form Genco is typical of Basilicata and also has a presence in Campania, Sicily and Calabria, where it would derive from the Calabrian word jencu, meaning "young bull"; Miranda attributes this same hypothesis to the scholar Vezzelli.