The authors differ on the origin of the surname. F. Miranda proposes an origin linked to leather work: the surname would derive from the medieval Greek byrsias and from the late Greek byrseús, a term that designated the tanner. The Sicilian dialectal term bburza or vurza comes from the Greek —also Latin— bursa, with the sense of "skin, leather". Miranda also notes that the nuclei present in Rome, in the Milan area and in the Como area could have an alternative origin in the medieval name Bortius, derived from the gentilic name Portius.

V. Blunda, on the other hand, considers that it is a Sicilian surname of Germanic origin, derived from the personal name Bord, linked to the root bord, which in its military sense designated the shield of the warrior. Blunda observes that the ending in -zi is typical of southern Italian and reflects the phonetic adaptation of the Germanic consonantism to the Sicilian Romance system.

The form without accent —Borzi— is the most widespread in northern Italy, although Miranda documents its presence also in Sicily, in the Catania, Messina, Syracuse and Ragusa areas, as well as in Lazio, Apulia, Basilicata and Sardinia.