The authors agree that this surname has as its base medieval auspicious names. E. De Felice notes that it derives from Avanzo, in the old sense of "acquisition, gain, advantage", referring to a desired and awaited child, and from Avanzato, with the old meaning of "increased, well grown". He adds that, in part, it may be the abbreviated hypocoristic of the auspicious name Diotavanzi, frequent in the Middle Ages, with the sense of "may God make you grow well (in the physical and spiritual sense)".

E. Rossoni provides a complementary perspective: he notes that the surname derives from the medieval Latin name Avantius or Avancius, documented in Mori (Trentino), and that in some cases it may come from Avanzino, obtained by aphaeresis of Diotavanzi. He documents the form Avanzini in the Como area around 1400, with the notary Giorgio Avanzini, and at the turn of the 15th and 16th centuries with the poet Hieronymus Avantius Veronensis. As for the geographical distribution, Rossoni places the surname mainly in the areas of Rovigo and Ferrara, with a cluster also in the Naples area; the variant Avanzini is concentrated in the Parma area and the area between Brescia, Mantua and Verona; Avanzino is typical of the Genoa area.

De Felice also records the forms Avanzati and Davanzati, especially present in Tuscany, and the patronymic D'Avanzo, documented in the Naples area.