I agree. My name is quite simple and doesn't sound strange with Spanish pronounciation. However, I know people who pick a similar name in their second language or who shorten their name so it can have the new pronounciation. I definitely think you want to introduce yourself with a name or nickname that is easily pronouncable by Japanese speakers, maybe just going for the last syllable of your name "Lyn," or similar.

I am Japanese, and my real name is AKIHIKO, but it is often hard to pronounce for foreign people. So I always tell them "Hello, my name is Akihiko, but just call me AKI". I think AKI for Akihiko is the same as Bill for William. You should find your simple name so that not only Japanese but any other people can call you easily. But "Gwen" is not hard for me to say and remember. I would call you "グウェンさん"

I don't think your name would be hard to pronounce for Japanese because it doesn't have sounds they don't have (they'll probably say 'Gwendoleen', though). It would be unfamiliar though and as it's a little long, a short version; Gwen, would be easier to remember. :)