The surname Acquisti is uncommon and is concentrated mainly in areas of Tuscany and the Veneto-Emilia axis, though it presents southern forms such as Acquisto and the patronymic D'Acquisto, the latter frequent in western Sicily. According to E. De Felice, it derives from a medieval personal name of congratulatory and auspicious character, Acquisto, formed from the noun acquisto ("acquisition"), used to designate a much-awaited and longed-for child. It can also be linked to the abbreviated form of the name Bonacquisto ("good acquisition"), documented as early as the Middle Ages, for example in Florence in 1260 as Bonacquistus.

Along the same lines, E. Rossoni agrees that these surnames derive from a medieval name of gratitude given to particularly longed-for children. He adds that, in some cases, they may come either from the abbreviated form of Bonacquisto or from place names such as Acquisti (in the area of Grosseto), which also introduces a possible toponymic route in their formation.