Scholars agree that this surname — along with its variants Isacchi and Isacchini — derives from the Hebrew given name Yiṣḥāq (Isaac), meaning "the smile of God." A. Bongioanni adds that the name may also be interpreted as "he upon whom God smiles," and notes that the Church celebrates as many as twelve saints of this name, mainly Eastern, with a feast day on March 25.

E. Rossoni specifies that the surname forms derive, directly or through diminutives, from the Italian given name Isacco, today fallen out of use, and does not rule out a direct Hebrew origin in some cases. It is also noted, from a separate source, that the surname may in certain instances derive from the word sacco ("sack, bag"), used to designate someone who made, transported, or loaded sacks — though a derivation from the given name Isaac is equally acknowledged.

Bongioanni further cautions that in surnames such as Sacchi and its derivatives (Sacchetti, Sacchini, Sacconi), the influence of the given name Giacomo should also be considered as an alternative etymon.

According to Rossoni, the variant Isacchi is concentrated in the area comprising the provinces of Bergamo, Como, and Lecco — with a presence in localities such as Barzago, Valmadrera, Cisano Bergamasco, Brembate di Sopra, and Suisio — as well as a pocket in Montepulciano, in the area of Siena, and another between the areas of Viterbo and Rome. The variant Isacchini is considerably rarer, documented in Pozzolengo, in the area of Brescia, and in Guidonia Montecelio, in the area of Rome. The form Isacco used as a surname appears in Rogeno, in the area of Lecco, in the area of Caserta, and in Taurisano, in the area of Lecce.