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Is it bad if you introduce yourself to a girl but she doesn't give you her name?

2-part question:

I made eye contact with this cheerleader on dance team at a basketball game and she seemed to be sending me good signals in return, so I decided to introduce myself after the game. When I approached her, I said "Hi, I'm (my name)". She shook my hand but didn't say her name in response.

Is that necessarily a sign that she's not interested and I was mistaking what she was doing as flirting, or could she just be intimidated by the directness of my approach?

The other part of the story is I wanted to ask her out but she was going home and seemed to be in a rush to leave. I only got to say I enjoyed watching her perform and she caught my eye. Basically, she said thanks and told me she hopes I come to future games. Later, I noticed her parents were waiting for her not too far away and probably saw me talking to her.

Is there enough to tell whether she's interested but just caught at a bad time or plain not interested? The next game's in 9 days, so should I got back and ask her out?
Is it bad if you introduce yourself to a girl but she doesn't give you her name?
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