E. Rossoni notes that it is a very infrequent surname, peculiar to Friuli-Venezia Giulia, of Slovene origin. He derives it from a nickname based on the diminutive of the Slavic term hlod, which means "tree trunk", possibly alluding to the robust build of the founder of the lineage.

B. Zuanella deepens this etymology and confirms that the base is the Slovene noun hlod, in its diminutive form hlodič, used probably as a nickname before becoming a surname. He notes that the surname Clodig pre-existed the homonymous place name, and not the other way around: the place received its name from the family that inhabited it. As a comparative reference, he mentions the surnames Čojovi and Čojaci, present in nearby localities and derived from the Slovene dialectal noun čoja ("tree stump").

According to Zuanella, the surname was spread in the 17th century along the upper valley of the Rieca/Rieka torrent, in localities such as Grimacco, Liessa, Brida, Peternel and Potok —a place name today disappeared and replaced by Pačuh/Paciuch—. Already in 1912 only three families with this surname remained in the comune of Grimacco, concentrated in the locality of Clodig, the current seat of the municipality.