Is Omegle, the chat website, safe?

[Anon]

I was chatting on Omegle and met this really nice guy. We seemed to have a lot in common and he didn't ask for pictures or ASL or anything. But then he asked for my name, and I gave him my first name. Then he said, "Well, (first name) (last name), can we keep in contact?" My question is this: How did he get my last name? I never gave it to him. He said he had my phone number and said we should meet "for real". I may be over reacting, but I'm scared. Can he really get all that information from thirty minutes of chatting?
I'll say again: I never gave him my last name or my phone number. Am I over reacting?