According to E. Rossoni, the surname Accogli would derive from an abbreviated form of the medieval name Bonaccogli, used as an auspicious name and given to particularly longed-for children, which suggests that the surname was formed from the name of the founding ancestor.

For his part, F. De Laurentiis notes that it is a rare surname, which may derive from the Italian verb accogliere ("to receive, to welcome, to host"), in allusion to an awaited or well-received child. More frequently, he interprets it as a hypocoristic of forms such as Benaccogliere or Benaccòlto, reinforcing its auspicious character within the medieval onomastic tradition.