The authors agree that this surname has roots in the orographic lexicon, that is, linked to the description of the terrain, and rule out the derivation from the Italian colla in the sense of "glue" or "adhesive substance". The connection with the word that designates "hill" appears in all the sources, although with variants according to the region.

The surname is linked to place names such as Colazza, La Cola or Collalunga, where the feminine form of the Italian colle ("hill") is recognised, from the Latin collis. In the Alessandria area the corresponding term is giogo del colle. E. Rossoni proposes that it could derive from nicknames related to place names that contain the word Colla, documented in the Massa-Carrara, Catanzaro and Messina areas, and identifies several clusters of origin in northern Italy: the Parma, Treviso, Genoa, Alessandria and Asti areas, with a possible additional cluster in western Sicily.

V. Blunda analyses specifically the Sicilian variant and indicates that it comes from the dialectal word còdda, with the meaning of "hill" or "small mound", a term peculiar to the dialectal orographic lexicon that designated the low elevations characteristic of the agrarian landscape of Sicily. According to Blunda, the surname could have originated in a minor place name referring to the place or to the one who resided on those elevations.