Ohhh man. You can completely turn this around on her and you clearly realize that, awesome. Girls hate it when men break trust with them (and generally walk away), and this is exactly what she did to you. She's given you a huge card.
You: "Hi Melissa. This is John from the other night at bla bla something charming"
Her: "*giggle* bla bla"
You: more charm
Her: *I like this guy, giggle* "Actually I have to tell you something, my name is actually Metilda"
You: Dramatic Pause
Her: "hello?"
Scenario 1
You: "That's a God-awful name. I can see why you give out a different one."
2
You: "Gee..well....that changes things. I swore to myself I'd never date girls named Metilda"
3. Combine 1+2
You: "Ew, Um.. I really don't know if I can see you now. Metilda reminds me of the old toothless lunch lady that made me cry when I was in 1st grade" <- say it in a funny way, or else she'll be real offended. Even though she's the liar, go figure.
4.
You: "Oh God. You're one of them. *pause*
Her: "one of wh... *cut her off*"
You: "Look, I pride myself on the fact that I don't lie to people, and I expect the same from anyone I have a relationship with. Thanks for finally come out with this, but I don't know if I can trust you now."
Her: "No really I'm not usually like that bs bs bs bs bs bs"
You: Some Time Constraint, then "see you around. Bye"
I like 4. She will call back because you're the exception to the rule. She is now in your reality. She's in the dog house. #4 is the most alpha. She will probably never give you **** again, because you showed no fear of walking away. But to pull off #4, you have to have no fear of letting her go.
Also, you may want to just think: Do I really want to be with a liar like this?
Good luck bro,