If your name reflects what you feel, then why wouldn't you chance a meet?
What is the worst thing that could happen? You have a terrible time, say your goodbyes and move on.
What is the best thing that could happen? You are no longer single and you actually enjoy spending time with this girl.
If your worried - do something small like go out for coffee or have lunch instead of dinner - have plans afterwards so you have a reason to leave. Like if you have lunch - you need to get back to work. If you enjoy yourself - give her a call back and do something where you invest more time.
Either that or find a reason to not go on a date with another girl.
Oh and she may have a different last name on facebook because she wants to protect her privacy for a variety of reasons - including she doesn't want crazy guys finding out who she really is and stalking her - to she just doesn't want people on facebook to know all her personal stuff.
Why don't you have your real first and last name on here? Unless of course your name is Single Sucks.