It appears that the majority of people with the name Gott/Gotts were not wealthy enough to leave many early records in the typical sources for land and taxes. By my calculation there should have been c 65 people in 1400 with the surname, and we do not see enough records supporting that in classes that paid tax and held land. (See here)
Given that surnames were not known to be in common use outside land owners prior to the 1400’s, linkages from these references to modern families have not been substantiated.
The spelling of the name has many minor variants: when you are not literate yourself, you rely on others recording it correctly. We have shown this doesn’t always work. And over time the name can change due to the way it is used, leading to the extra ‘s’, so it does not make sense to draw significant divisions between the names based on spelling. Geography would make a more sensible division, with Yorkshire, Lincolnshire and Norfolk being the main areas.
One thing is clear: the name is not a recent import direct from Germany, despite it sounding German. I have no records of anyone from Germany taking the name in UK. If you look at the surname distribution in Germany itself it is very small.
Given that there are more early records for the surname GOTT in Yorkshire and Lincolnshire, that provides more options for how the name came into Norfolk:
Are the people not connected by anything other than a name based on where they lived?
Did they all come into the area through the Danish and Viking settlement at the same time?
Did the Yorkshire Gotts trade down into Norfolk as Ian Gotts of Kings Lynn suggests? And then their name metamorphosed into GOTTES?
The name may derive from old terms for water, drainage, possibly people’s appetite/size, etc:
The possibility of it coming from Ashkenazy Jewish words has no evidence for the surname as a single word, though it might apply in Germany as a compound word, eg Gottschalk.
Gocelin as an old French source may lead to Gots as a first name, but is needs it to be used regularly with a hard ‘c’ ‘Gotselin’ to have credibility and there isn’t a body of evidence to support this. Most references for its use show it going to a soft ‘c’, hence Gosselin, so this makes it a difficult proposal in the wide context of three counties.
For the name to be a personal nickname for corpulent people may apply to individuals, but there is no easy way to see how this would develop into a hereditary surname across three different counties.
Water/drainage/mill chases are a common theme whatever the county, and these three areas were all under Scandinavian rule, so the likelihood is high that the name comes from their language. But with early records it may be a transitional name, used when people were residing near water, until 1350 onwards.
For names earlier than 1400 I now do not expect there to be family connections unless there is land, assets, wills, or a clear tree. Neither will I spend time looking for connections!