Just a short description...
In my country among most Chinese, a woman can choose to change their surname/family name to match her husband. For example, Linda Ng marries Andrew Lee (both are not real people). Linda would change her surname from Ng to Lee, and therefore becomes Linda Lee. She can be still known as Linda Ng, but to keep it simpler for other people, she takes her husband's surname and becomes Mrs. Lee instead of Mrs. Ng.
...uh, do I make any sense you y'all? xD
Anyways, sure. I'll take my future husband's surname, no problem with that. I would still want to be known with my own surname though. I'd feel quite weird without it.