The authors agree that this surname derives from the place name Randazzo, a locality of the province of Catania, in Sicily, and that its distribution is predominantly Sicilian.

E. Rossoni notes that some researchers have proposed an alternative derivation from the Byzantine name Randaches, although he considers this hypothesis very improbable.

F. Miranda develops in greater detail the possible etymologies. The place name Randazzo appears in the sources as Randacium in Latin, Randàkion in Byzantine Greek and R'andag in Arabic, which reflects the multicultural history of Sicily. Miranda also considers that the surname could go back to the Greek-medieval personal name Rendakès or Randakés (Ρενδακης), linked to Byzantine patricians. Among the additional hypotheses, he mentions the Sicilian dialect Grannazzu or Rannazzu, a variant of ranni ("big"), and the term randa, which designates a livestock enclosure, alluding to a first bearer who owned a large corral.

E. De Felice records it as a surname of high frequency in Sicily, without proposing an additional etymology.