Re: German origin of name day
This is not relevant to the origin of the surname Day, but to the origin of the surname Tagg, which you suggest might be a german connection.
I live in Scotland and although there are some local Tagg's in my community 200 years ago I've not managed to trace any of mine back anywhere except lincolnshire in England. However I remember sticking the name Tagg into an internet surname database which suggested the name might be Pictish and from Ross-shire.
It's funny because one of the first battles where the Scots (invaders from North Ireland about 1,000 years ago) defeated the Scots were in the surrounding hills. Having moved here from the south it definitely feels weirdly like home - and I keep telling the Scots that they are the invaders!