E. Rossoni proposes that Angemi is probably an abbreviated form of the surname Cangemi or Cancemi, with documented presence in San Giovanni la Punta and in the areas of Catania and Messina.

F. Miranda develops this line in greater detail: he considers that Angemi results from an aphaeresis —that is, the suppression of the initial syllable— of Cangemi or Gangemi. These surnames would in turn derive from a place name, such as the locality called Cangemi in Termini Imerese, or from the Latin cognomen Cangemius, attested in the 17th century with the physician Franciscus Cangemis. Miranda also takes up a hypothesis of Arabic origin: the word haggam, which designated the "applier of leeches" and, by extension, the barber, surgeon or healer, which would suggest a nickname referring to the trade of the founder of the lineage.

As for its geographical distribution, Miranda notes that the surname is very uncommon. Its main cluster is concentrated in Sicily —with presence in the provinces of Catania, Enna, Messina and Syracuse—, with small clusters also in Puglia, Liguria, Tuscany and Calabria.