The authors agree that this surname is of Lombard origin and is linked with a dialect expression relating to the cow. It derives from the medieval name Maliavaca, which would mean "cow-eater", and the base word comes from the Latin magulum ("mouth" or "muzzle"); the surname is documented from the 13th century in localities such as Monza and Milan, with variations in the initial syllables over the centuries.

E. Rossoni places the surname in the area between Milan and Pavia, and derives it from the archaic dialect nickname majavaca ("he who eats cows"). He proposes, however, a second interpretation as well: the term is said to have been formed from the dialect imperative muglia ("milk!"), later altered into miglia, giving rise to an expression that would mean "milk the cow". This is the reading preferred by R. Brondolo, who rules out the variants "strike the cow" or "eat the cow" and considers the form muglia la vaca, that is, "milk the cow", more coherent.

In sum, the surname reflects a nickname of imperative origin documented as early as 1220, whose exact meaning —"eat the cow" or "milk the cow"— remains a matter of debate among specialists.