Should the wife and child in a marriage have the last name of the father?

Me and my girlfriend are debating if a women should have to take the last name of her husband in marriage. She believes that a women has a choice on whether to take the last name of her husband. I believe that the wife should have the last name of the husband. I know it may seem a little old fashion but I just think that tradition is dying and I like tradition. She thinks I'm sexiest but I'm just a believer of that tradition. I just think its stupid to get married and not take the name of your husband. I mean whats the point of getting married if we just gone keep everything the same and change our relationship status like a facebook mood.