Adoption, step-children, or foster children are three I come up with.Or mom got married/re-married after her son was born. Or took her maiden name back after a divorce.
When my niece was born her mom and he agreed that if she was a girl she would have mom's last name, a boy would have ours.
-Eric
Or the mother continued to use her maiden name after she was married. That's not all that uncommon these days.