Tate

Tate is derived from the Norwegian Tait. Middle English version is Taten.

From middle English meaning 'cheerful'.

As I understand it from my reference books (A Dictionary of English Surnames by Reaney & Wilson, for instance) technically it is the surname Tait that goes back to the Old Norse word for "cheerful", while Tate goes back to an Old English name, Tata, the original meaning of which is unknown. Since Tait and Tate are pronounced identically, I'm sure over the centuries there has been some confusion in spelling and some "Tate" families may originally have had medieval ancestors with the Old Norse name. But the origin does seem to be a bit more complicated that just "Old Norse" for "cheerful". [noted -ed]