The authors agree that this surname derives from the medieval name and nickname Moro, which in turn continues the Latin cognomen Maurus, with the meaning "inhabitant or native of Mauretania, of North Africa" and, in a figurative sense, "of very dark skin or complexion". During the Middle Ages, the term further took on the new meaning of "Saracen", that is, one belonging to the Muslim populations of the Mediterranean.

E. De Felice notes that in some cases the surname may reflect place names such as Morello, Moretti, Morino or Morozzo. He adds that the forms Morassi, Morassutti, Morati and Moratti, apocopated variants, are proper to Veneto; that Morozzi is concentrated in Tuscany, and Morero in Piedmont.