B. Zuanella notes that this surname arose through the diminutive suffix -ko, frequent in the formation of Slovenian names and surnames (Slavko, Benko, Mirko, Janko, among others). The most solid hypothesis was formulated by I. Koštial, who proposes that the surname was formed from the aphaeretic variant Trine of the hagionym Catharina, with the addition of that suffix. Zuanella warns that it should not be confused with the surname Trink, diffused in Slovenia, nor equated without foundation with the surname Trincho, typical of Andreis, in the Pordenone area, whose original form was Trinch in the 16th and 17th centuries and only later was Italianized.

E. Rossoni agrees on the essentials: the surname derives from a hypocoristic formed on a contracted variant of the name Katerine, with the Slavic suffix -ko of diminutive value. Rossoni locates the surname mainly in the Udine area —in particular Cividale del Friuli— and in Andreis, in the Pordenone area; while the graphic variant Trinko he considers specific to Trieste.

Zuanella specifies that the surname is documented for at least five hundred years in Cepletischis of Savogna and in the locality of Trinco, near Drenchia, in the Valli del Natisone, a zone of Friuli-Venezia Giulia. From there it spread to neighbouring localities and, after the Second World War, also outside that area. The form has remained stable over time, though the documents record graphic variants such as Trinko, Trincho and Trinco. The surname is also present in Slovenia, in the form Trinko, for example in Ljubljana and in Maribor.