Not keen, because to me it's a surname with a masculine ending. I do prefer
Madeleine. However,
Maisie might make a suitable nickname. I know it's a Scottish pet name for
Margaret, but I don't see why it can't work as a pet name for
Madison. And it's quite fashionable at present, but not too commonly used. As for your friend, she sounds like an immature brat. Don't let her worry you.