The sources differ in the origin of this surname. According to what is recorded in Surnames in Italy, it is a surname of anthroponymic origin —that is, derived from a personal name—, probably coming from Gaufer, meaning "chief of the people", and linked to the Sebino zone, the basin of Lake Iseo, in Lombardy.

Another source, on the other hand, proposes an Arabic etymology: it would derive from ghaffār, an intensive active participle of the verb ghāfara ("to forgive"), with the sense of "very forgiving". With the definite article, al-Ghaffār is one of the 99 names of Allāh in the Islamic tradition, part of the triad referring to forgiveness together with al-Ghāfir and al-Ghafūr. Both hypotheses are not necessarily exclusive, since the form Gaufer could in turn have a Germanic root influenced by contacts with Arabic in the medieval period.