Lovely day in the country

I got up to my dad's country house in the mid-afternoon. The weather up here is so much better than Montreal, and the pace is nice and slow.

I went for a swim in the lake, had a lovely steak dinner with my dad, and now I'm just enjoying the peace and quiet. Yay, country!

SCA name question

I've got a question for the Viking / Norse enthusiasts among my friends' list. You know who you are.

There are names out there that shift depending on the region. "John," for example, becomes "Jean" in French, "Giovanni" in Italian, "Juan" in Spanish, and so on.

What would be the correct permutation of "Katherine" for 10th-12th century Denmark? Any ideas? (Super-wonderful bonus points if you can come up with something equivalent for the byname "Ashewode.")

Thanks!

Edited to add: A bit of Internet searching seems to indicate that "Katherine" in almost any form would not have existed in Western Europe before the Crusades, since it was brought back from the East by the Crusaders. In other words, trying to fit it into 10th-11th century Denmark -- in any form -- is a losing battle. Is that accurate?