If you supported a law to require that a woman takes their husband's last name upon marriage, then perhaps. Otherwise, not really. You can support the traditional ways without thinking that everyone must be forced to comply with them.
^ I agree with this ^
I'm quite a lot like this on a number of issues. I personally believe that if you promise someone "til death do us apart" it should be til death do us apart, that doesn't however mean I want to outlaw divorce or make divorce harder. Same with surnames, I think it's proper that one of the spouses should take the others last name when they marry, I do not believe in making that the law.
It's not very strange at all actually. No more than the fact I believe that everyone who can do it is morally obliged to give blood, but I would still never support a bill that forces people to give blood.