E. Rossoni places the origin of Cocchi in the zone of confluence between Emilia and upper Tuscany, with presence also in Lombardy and in Lazio. He considers it a patronymic derived from the medieval personal name Coccus or Cochus, to which he attributes an affectionate value, equivalent to the Italian cocco or coccolo, terms used to refer to children or loved ones. This name is documented in the Annales Pisani under the year 1159 and in the Diplomatic Code of medieval Lombardy in a deed of 1192.

P. Canè notes, with greater caution, that the surname could derive from "cocco" with the sense of "dear", although he also suggests the possibility of a relation with the term "egg", without ruling out other origins.