The authors agree in noting the Greek origin of the surname. G. Rohlfs links it to the Greek surname Kutrìs, relating it to the Byzantine presence in southern Italy and the survival of Greek onomastics in Calabria.

V. Blunda, for his part, derives it from the Greek coýtra, meaning "head", and proposes that the surname would have arisen as a nickname applied to an ancestor for some trait associated with that part of the body. Blunda records this form in the Sicilian context and notes its parallelism with the variant Cutrì, to which he attributes the same root.