Gaut is an early Germanic name, from a Proto-Germanic gautaz, which represents an origin myth national god of a number of related Germanic peoples of the migration period, a period starting from the period when it affected the Roman world, running from about the 5th to 8th centuries AD.[5][6]
Gautaz derived from the Proto-Germanic geutaną, meaning "to pour" which could allude to watercourses in the land where they were living.
This same root may be connected to the name of the Swedish river Göta älv at the city of Gothenburg. The earliest mention of the Geats was possibly made by Ptolemy in the 100s AD ("doutai" or "goutai") or in the 500s by Jordanes ("gauthigoth") and Prokopios ("gautoi")
Both the migration period Goths and the Scandinavian tribe of the Gutes (the Gotlanders) were called Gotar in West Old Norse, and Gutar in East Norse (for example in the Gutasaga and in runic inscription on the Rökstone).
According to the rules of Indo-European ablaut, the full grade (containing an *e), *gʰewd-, might be replaced with the zero-grade (with the *e disappearing), *gʰud-, or the o-grade (where the *e changes to an *o), *gʰowd-, accounting for the various forms of the name. The use of all three grades suggests that the name derives from an Indo-European stage; otherwise, it would be from a line descending from one grade.
It survives in the modern Scandinavian tribal name Gutes (Gutar in Gutnish, in Swedish Gotlänningar), which is what the inhabitants of present-day Swedish island Gotland in the Baltic Sea call themselves. Another modern Scandinavian tribal name, the Geats (in Swedish "Götar"), which is what the original inhabitants of present-day Götaland (originally south of Svealand, north of the former Danish regions Scania and Blekinge and east of the former Dano-Norwegian regions Bohuslän and Halland) call themselves, derives from a related Proto-Germanic word, *Gautaz (plural *Gautôz).