The scholars consulted agree that this surname derives by aphaeresis from the medieval auspicious given name Buonaggiunta or Buonaggiunto, meaning "welcome" or "good addition," and referred to a hoped-for and desired child. The full form is documented in the 13th century with the Lucchese poet Bonaggiunta Orbicciani, cited by Dante Alighieri in canto XXIV of the Purgatorio. The source Surnames in Italy similarly traces the surname to the old given name Bonagiunta or Bonaggiunta, analyzing it as a compound of bono, "good," and aggiunto, "assistant."

F. Miranda adds that the name may also have carried the sense of "addition, assistant, or relative," and notes that in the Sicilian dialect ggiunta means "what is added to something" (also rendered as iùnta). E. Rossoni documents the transformation into a surname in Florence from the 15th century, citing the master builder Meo di Piero Giuntini, and notes its continuation into the 16th century with the well-known Giunti family of publishers.

Regarding geographical distribution, Rossoni indicates that Giunta has its main concentration in Sicily, with additional areas of origin in the regions of Pesaro, Lucca, Milan, and Turin. The variant Giunti is characteristic of Tuscany; Giuntini is concentrated in the areas of Florence and Pisa; Giunto is associated with Campania; and Zonta appears in Veneto and Friuli-Venezia Giulia, especially in the area of Vicenza. E. De Felice notes that the surname is most frequent in southern Italy, particularly in southern Calabria and Sicily.