E. Rossoni and V. Blunda agree that the surname derives from a Germanic compound formed by the elements ric/ricja ("power, domain") and mund/munda ("protection, tutelage").

Rossoni distinguishes the forms: Rigamondi is very rare and typically Lombard, especially of the Milan area; Rigamonti, more diffused, is distributed in the area comprising the Milan, Como, Lecco and Bergamo areas, with good presences also in the Varese and Brescia areas.

Rossoni specifies that they derive from a variant of the medieval name Richamundus or Rigamundus, derived from the Germanic Richmundus, documented in a medieval text of the beginning of the 14th century.

Blunda, for the Sicilian variant, derives it from the Germanic compound Ricja Munda, with the meaning of "protection of power" or "tutelage of the domain."

Blunda notes that the association between power and protection reflects the ancient Germanic conception of legitimate authority as the active capacity to guarantee the security of the members of the group, particularly expressed in the institution of the Lombard mundium, where the head of the family exercised legal tutelage over the women and minors of the line. He adds that, as a surname, it is preserved widely in Lombardy.