Your male line is such a small part of your ancestry. Go back 20 generations, say 1400, you have a million ancestors, and only one of them was a Wray. So you can't assume your grandfather's eyes and hair came from him.
Actually it's overwhelmingly likely that you inherit no genes at all from that Wray of 1400. You only have 30,000 genes, and a million into 30,000 doesn't go.
It would be different if England were divided into separate ethnic communities which married only amongst themselves. If you find a Jewish ancestor, you'll have lots of Jewish ancestors. But England was never like that. Apart from Jews, to some extent, all invaders and immigrants have intermingled and intermarried, as in the U.S. So a man's surname was never much of a clue to the origins of his wife and mother.
That 1400 guy was probably called del Wraa, or something like that. Almost certainly his ancestor who adopted that surname was the tenant of a hill-farm called "the wraa" locally. There will have been a number of farms called that, scattered around the north of England, and several unrelated tenants who independently took the name as a surname.
Nothing can be said at all about the origins of those tenants. It can't be supposed that they were Vikings just because the word itself is Norse.
Basically English is English. They were already all mixed up long before most people had surnames.
Lots of families have a Norman knight story, but few if any are true.