Votadini is the Latin version of the name which dates at least to the 2nd century when the tribe appears on Ptolemy's map of Britain as the Otadini. The early middle ages spelling of Guotodin reflects the loss of case endings typical of the time. Another example of this are two towns called Venta. Both lose the 'a' to become Caer Went and Caer Wynt. The Went element in Caer Went was retained in the modern village of Caerwent in south Wales but it changed spelling to Gwent to refer to the region of that name.
Initial v in Brythonic often ends up as g or gw in later Brythonic languages. Hence Vortigern appears in Old Welsh as Guorthigirn and modern Welsh as Gwrtheyrn. This is the same with Votadini to Guotodin and then Gododdin.
There's no reason to think that the Votadini/Gododdin who are counted as a Brythonic tribe by the Romans and later included as one of the Brythonic peoples of the Hen Ogledd (the Brythonic kingdoms that existed in northern England and southern Scotland during the early middle ages) were anything other than a Brythonic people. A group of Gododdin under their lord/king Cunedda settle in Gwynedd after defeating and apparently expelling the Irish that had settled there.
It would be odd for a Brythonic tribe to have a Germanic god as their namesake.
When the Angles did arrive they brought their paganism with them and one of the gods they worshiped was Woden, not Odin. Edin's Hall Broch in Berwickshire retains the name and while Edin suggests Odin the older names of Edin Hall show it to come from Woden. Likewise Woden Law in the Cheviots shows the Angles worshiped Woden not Odin. Wednesday also shows the Angles and the Saxons worshiped Woden. Modern Scandinavian languages call their Wednesday Onsdag after Odin. Odin worshipers don't show up in the territory of the Guotodin until the mid 9th century when the Great Heathen Army overruns Northumbria.
As the Anglian conquest of the former Guotodin lands appears to have been completed around the mid 7th century with the capture of Din Eiddyn (Edinburgh) there's around 200 years of Anglian rule before the vikings show up with their Odin.
Woden is considered to be from proto-Germanic *wōdaz (the asterisk means the word is hypothetical) related to proto-Celtic *wātis which gives Gaulish Uatis. This was a class of seer mentioned by the Romans as being a rank/division within the Druidic order. Modern Druids use the similar word Ovate. The welsh word gwawd comes from the same origin with that initial v/u becoming a gw. Gwawd though has taken on a negative connotation of satire, scorn instead of the original poetic/seer meaning it originally had. The point of all this being that if the Guotodin had been named for Odin/Woden then it's more likely the connection would involve a word closer to gwawd than the od in Guotodin. Woden/Odin being gods of both poetry and divination which the Celtic druidic classes of Uatis, Ovates, Old Irish Fáith and Welsh gwawd do likewise showing that common Indo-European tradition. The Vatican in Rome is another example of this group with the name deriving from the ancient Roman vates who were diviners.
