Can I find out who is +1ing my website?

I don't think I've seen anything about a full-on reporting utility around +1s. (Yet?) But if what you're looking for, like site name, is unique enough, you can fudge this a bit with a site-limited search, eg.

But that requires that users have made their +1s public so they show up in the tab, and also searches across their entire profile, so you'll also get people who have the term in their Posts or Buzz tabs, too. Depending upon whether you specifically want only +1s or just want to see who's supporting you, that may not actually be a bad thing. Obviously people who aren't publicizing their +1s won't be returned by this, but then they probably wouldn't be by any other method either, I guess.

Just last week, someone in the Google Webmaster forum suggested it'd be possible to grab identities through the button and a Google employee popped in basically saying "okay, prove it." Given it would've been simple enough for him to just confirm(if that were the case), I'm going to guess the real answer to your question is either no, or that it at least shouldn't be possible at the moment.