The two scholars consulted agree that Morassi originated as a nickname before undergoing transformation into a surname. E. De Stefani traces the form to the Friulian moro, meaning "one who has black hair," with the addition of the suffix -às, which carries a pejorative or augmentative value. De Stefani documents the nickname from the mid-fourteenth century, noting that for centuries it also functioned as a given name. He further identifies Brunasso as a related surname sharing the same etymon.

E. Rossoni agrees that the surname grew out of a nickname but offers two possible starting points: the physical appearance of the founding ancestor — specifically, a dark complexion — or the archaic Venetian dialect term morasso, which designated a bit or implement used with horses and oxen to keep them under control.

Geographically, De Stefani documents the surname across several localities of Carnia, the mountainous area of northern Friuli in the province of Udine, including Paluzza, Piano d'Arta, Cedarchis, Cercivento, Ravascletto, Sutrio, and Cadunea. He also notes the frequency of the related form Moras at Porcia, and the variants Morassut and Morassutti at Cordenons. Rossoni places Morassi primarily in Friuli-Venezia Giulia. He additionally observes that the variant Morasso is concentrated in the area of Genoa, with a smaller presence in the area of Venice. It is also recorded as a surname typical of the Sicilian municipality of Santa Croce Camerina, in the province of Ragusa.