E. De Stefani places the origin of this surname in the Carnia, a mountainous zone of the north of Friuli in the province of Udine, where it is attested in Prato Carnico, Rigolato —especially in the frazione of Ludaria— and Forni Avoltri, with documentation in the Gorto canal from at least the end of the 15th century. He considers it a microtoponymic surname derived from the Friulian agâr, in turn from the Latin aquarium, a term that in several zones of Friuli designates the furrow or drainage channel, and that in the Carnia was used specifically for the bed of a watercourse —frequently dry except in heavy rains— together with its two banks. The place name Agarìnas, in the comune of Prato Carnico, is recorded today as a locality of fields with no visible trace of water, preserving the fossilised memory of an old course.

De Stefani also notes a derived form, Agarinis, with the Friulian diminutive suffix -inis, concentrated in Ovaro: the place name Agarinis appears attested in Ovasta —a frazione of Ovaro— from the end of the 14th century, and the surname is documented in Mione —also a frazione of Ovaro— from the end of the 15th century. He frames this surname within the wide Friulian onomastic layer derived from hydronyms, well represented in Carnic anthroponymy.

E. Rossoni proposes, on the other hand, an alternative derivation from the medieval name of Hebrew origin Agar, documented in a deed of sale of the year 759. He also considers possible a link with a disappeared Friulian place name called Agaro, or with a nickname, since agar in dialect means "furrow" or "ditch". Both authors agree in noting Friuli as the zone of rooting of the surname.