OK so someone asked for my mother's name and I told them my adopted mother's name since I was adopted when I was little. Can they use it for black magic purpose?

Does the person who asked believe in black magic? I don't.
But all that is beside the point. If you don't know someone well enough to know much about them, you shouldn't be answering any questions at all. These days people ask personal questions to find out about bank accounts and ways to steal your identity, or they are a stalker, or who knows.

Why would you assume they would use that information for magic against you?