Deanna Troi! That's who I think of, having grown up watching Star Trek the Next Generation. :)
I think it's a nice choice. (I assume you've nixed Danielle?) Deanna's not overly used (or really used much at all). It sounds perhaps a bit dated or modernly-old-fashioned, but I think it would be perfectly acceptable. You could even call her Danni, Anna/Anne, Dee, or even Danna, for nicknames, which are always good options to have.
Throw us out any other ideas you're having, and let us know what you decide on. Good luck!