The authors agree that this surname has a Greek-Byzantine origin and derives from a military and administrative title. E. De Felice describes it as an alteration of the Byzantine term turmárches, composed of turma —each of the administrative and military subdivisions of the themes of the Byzantine Empire— and árchein ("to command, to be in command"), with the suffix -árchēs. He notes that in Italy this organizational system had a particular presence in the themes of Sicily, Calabria and Lombardy.

E. Rossoni specifies that the office corresponded to the command of a troop of men (turma archè) and identifies concrete testimonies of its transformation into a surname: a deed of 1075 in Larino, in the Campobasso area, where a certain Maraldo Trimarco figures as a witness, and records of the 16th century in the Messina area with the notary Antoniello Trimarchi. Geographically, he places the form Trimarchi in the Messina area and in the Reggio Calabria area, while the variant Trimarco appears specifically in Buccino, in the Salerno area.

G. Rohlfs confirms the Greek-Byzantine origin and specifies the geographical distribution in Calabria: the city of Reggio Calabria, and various localities of the province of Catanzaro (Guardavalle) and of the province of Reggio Calabria (Laureana, Molochio, Palmi, Taurianova). He also records the form Trimarchi as a surname typical of the province of Messina, and the variant Trimarco in Naples. His definition of the etymon, turmarchis, he translates as "chief of a military squad, governor of a district", emphasising the double military and administrative character of the office.

P. Durante agrees on the Greek origin and on the root turmarkhes, which he defines as "commander of a cavalry detachment", an emphasis he shares with Rossoni and which complements the more administrative perspective highlighted by De Felice and Rohlfs.