Should I apologize for asking a woman a question that she doesn't want to answer?

I've been talking with this girl who gave me her phone number, but a fake name. She told me from the outset that the name was fake, so it's not that big of a deal.

I asked her for her real name at the beginning of this week, and she never responded. I suspect that the reason might be that she's uncomfortable with me asking her real name.

Should I apologize for asking?

You should apologize
There's no need to apologize
Apologizing would actually be a bad thing for you to do.
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Should I apologize for asking a woman a question that she doesn't want to answer?
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