Would you go on a date with a woman who won't give you her normal phone # or last name before meeting?

We have video called. I know she is who she says she is, but I feel weird taking someone on a date who could very easily make it so I could never contact her again if she decides she doesn't like me. Says she usually waits two dates. I guess if it goes well I'll ask her after the first. To me though this is also a no-go for any potential kiss, because if you won't give me your real #/last name, kissing is more personal...

Would you go on a date with a woman who won't give you her normal phone # or last name before meeting?
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