Forget it. It might seem like an innocent and easy way of “getting to know each other” – “My name’s …, what’s yours?”. But as everyone and their mom is doing that, it is just plain lame. If she’s not interested in you, she’ll forget your name in an instant. And if she is, believe me, she’s gonna ask for it:) And this way it even becomes a little test of “am-I-getting-anywhere-with-this-girl?”:) If during the conversation she suddenly discovers to her amazement that “goosh, I don’t even know this guy’s name?!” and asks for it… you’re well on your way:)
Asking for her name is propagated by some on the pretence, that this way you’ll get to be “formally introduced”. And what is that supposed to mean? Now that she knows your name, she’ll be burning hot for you? Hardly. Rather, you get to be formally categorised as a chump, or maybe a “friend” if you’re lucky (believe me, you’re not if that is what happens:)
One more argument against asking for names – you ask for her name and then, oh goosh, you forget it!
She expects you to know it but you don’t. And “What’s you’re name again?” is not even a neg – where’s the compliment in that? You could of course go “Well, I know you had a very beautiful name… but what was it exactly?” – use this one to neg her if you asked for her name and forgot it. But better just forget trying to juggle with names and let her ask yours first. And see, if she remembers:)
In conclusion – names are fine as long as she initiates the exchange. Until then – remain a man of mystery:)