You can get away with calling her, "darling, honey, pretty lady, etc." for a good while.
Do you have her home phone number? You could try reverse telephone look up on the internet.
Get an invitation to her home and look for mail addressed to her.
Try the driver's license trick. Think of some cock and bull story as to why you needed to pull out your drivers license and tell her that the person told you it was a crappy picture ... ask her for HER opinion, while she's looking at it, you now have a good reason to ask to look at HERS.
Finally (desperate measure time) take her out and arrange IN ADVANCE to have a friend of yours be there. When YOU go to the bathroom have your friend come up and introduce himself to the lady, tell her he's a friend of yours, he thought he saw you ... as in, "HEY, was that Joe Smith you're with??? It IS, oh, hey, he's a buddy of mine, I'm John Doe," now since YOU'RE in the bathroom and this is a PURELY coincident chance meeting she, of course, has to introduce herself. Now when you come back from the bathroom what a surprise your old friend John Doe is sitting at the table with your girlfriend! He hangs for one drink then has to bail. Meanwhile, you turned off your cell phone so he can call you when he's out of eye shot and give you her name.
ONE of those has to work.