Are you disappointed? It depends on the situation, but I don't usually get disappointed by a girl not remembering my name. And I have an easy name to remember. If you are disappointed, then it will be harder to make it seem like it doesn't matter. But there are so many girls out there, you can't possibly remember them all, right?
Either way, you can make it seem like you aren't disappointed by blowing that first statement way out of proportion. "I CAN'T believe you DON'T REMEMBER my NAME. After ALL THOSE GOOD TIMES we had. I just don't know what I'm going to do with my life." And have an overly pained expression on your face that is comical in nature. Shows you don't really care and how silly it would be to care, which reinforces your second DHV statement.
Saying that her name stuck isn't clingy, it just demonstrates interest-in most situations. I'm assuming this is a girl you met at a bar or party or something pretty recently, and the whole set of occurrences in within a week. Otherwise, you're right. If it's been more than that, not only does it sound clingy, but it could be that it IS clingy (If that makes sense).
