The authors agree that the surname is of Greek origin and derives from the diminutive term elafàci or elafaki, meaning "fawn".

E. Rossoni derives it from a name or nickname based on the Greek term elafaki, a diminutive form of elafos ("deer").

V. Blunda, for the Sicilian variant, derives it from the etymon Elafàci, linked to the zoological lexicon of the wild world. He notes that the root élaphos ("deer") is combined with a diminutive suffix, and that the surname may have arisen as an affectionate nickname applied to an ancestor for his agility, his slenderness or his youth. He adds that the Mediterranean fauna provided the Greek-speaking world of Sicily with an inexhaustible repertoire of images for popular onomastics.