I perhaps have gone with more obvious names, like Kim. It's in Use in Asia, English speaking countries, and the Scandinavian countries. Although I have no idea if there is a transfer between English and Scandinavian languages, I doubt there is a direct connection to Korea.
Never heard of Zane outside of the USA, and Rukia I only vaguely remember hearing at all.
As for names that are coincidentally the same in different cultures, I am not really qualified to answer. You'll either need to get an expert or do quite a bit of research on that.
Probably easier if you give everyone reading the thread an idea of what you want to happen. It seems you want someone with a name that makes it hard/impossible to immediately pin down their ethnicity. If that is the case then I would suggest looking at names in the original ethnic group and picking one that suits that need.
What I do know from speaking several languages is that there are a lot of homophones, words that sound the same but can have different meanings, and those can be completely out there when they come from different languages.