Gautr, Gauti, Guti, Gothus and Geat are name forms based on the same Proto-Germanic root, *ǥuđ- (see God). Gapt is generally considered to be a corruption of Gaut.
The names may represent the eponymous founder of an early tribe ancestral to the Gautar (Geats), Gutans (Goths) and Gutes (Gotlanders). Gaut was one of Odin's names and the name forms are thought to be echoes of an ancient ancestry tradition among Germanic tribes, such as that of Yngvi, Freyr and the Ingaevones.
Moreover, the names Geats, Goths and Gutes are closely related tribal names. Geat was originally Proto-Germanic *Gautoz, and Goths and Gutes were *Gutaniz. According to Andersson (1996), *Gautoz and *Gutaniz are two ablaut grades of a Proto-Germanic word with the meaning "to pour" (modern Swedish gjuta, modern Danish gyde, modern German giessen; English in-got,gushing) designating the tribes as "pourers of metal" or "forgers of men".
The name Gautr appears as one of the names of Odin in Norse mythology, but also as an alternative form of the name Gauti, who was one of Odin's sons, and the founder of the kingdom of the Geats, Götaland (Gautland/Geatland), in Bósa saga ok Herrauðs (c. 1300). This Gautr/Gauti also appears as the father of the recurrent and undatable Geatish king Gautrekr in that saga, and several other sagas produced between 1225 and 1310.