F. Miranda notes that this surname is very widely diffused in Calabria and Sicily, with a presence also in other regions such as Lombardy, Piedmont, Lazio, Liguria and Tuscany. In Sicily it appears in all its provinces, with a particular concentration in the Catania, Messina, Syracuse and Palermo areas.

As for the origin, Miranda proposes a Greek etymology based on a process of deglutination —that is, the loss of the initial syllable de-— from the place name Diminniti, a hamlet of the municipality of Reggio Calabria. The original Greek forms would be Deménna and Demenníes (Δεμέννα - Δεμεννίης). Citing the scholar Macris, Miranda explains that this name corresponded to the Greek population of the Val Demone, which took refuge in Calabria during the Arab domination, and that in time the form Deminniti was reduced to Minniti, the complete form being preserved only in the locality Diminniti, on the outskirts of Reggio Calabria.

P. Durante also proposes a Greek origin, relating it to the word menitès, with the approximate meaning "irascible", although he presents this hypothesis tentatively and without further development.