F. Miranda notes that this is an infrequent surname which, together with its variants Tirenni, Tirenna and Tilendi, would derive from the Latin name Terentius or directly from the Greek Teréntes, the diversity of forms being the result of erroneous transcriptions. G. P. Holmes agrees on the Greek origin and links it with the given name "Terenzio".

According to Miranda, the surname is concentrated almost exclusively in Sicily, where it is typical of the Catania area —in particular in localities such as Maletto, Misterbianco, Bronte and Catania itself—, though it also appears in the Palermo and Trapani areas, and in the locality of Catenanuova, in the Enna area. Outside Sicily, Miranda records specific and occasional zones of the north and centre of Italy: Lombardy, Piedmont, Liguria, Emilia-Romagna, Tuscany and Lazio.