If you have presented your name to a girl it is very possible that she doesn't remember it a few minutes later. I have tried to make up reasons to name drop my own name many times and almost every time I see an expression in her eyes similar to "Ahaa! That was his name". After this moment she gets much more comfortable since, now, there is nothing left in the back of her mind keeping her distracted. She may now communicate more smoothly. In the case she already knew your name, the comment will pass by unnoticed.

I usually do this by telling her a story where someone calls my name, by imitating the conversation. It surprises me how much easier it is to lead the conversation if she is more comfortable and more focused on what you say.