The authors agree that this is a Sicilian surname. E. Rossoni places it specifically in the area of San Salvatore di Fitalia, in the province of Messina, and sets out several hypotheses on its origin. One possibility is that it derives from the Spanish surname Granja, linked to an agricultural establishment; another, that it comes from the Spanish granza, with the meanings of rice husk, madder, and coal in small pieces. Rossoni also considers a Norman derivation from the name Granza, documented in a 12th-century text by Saxo Grammaticus.

V. Blunda proposes a dialect explanation: the surname would derive from the Sicilian word grànza, meaning "fine bran", the residue of the sifting of wheat, a term proper to the vocabulary of the mill and the bakery. According to Blunda, the surname would have arisen as a nickname for the miller or baker who worked with second-quality flours.