"And doesn't that mean you have two legal identities then. "
No , as I think Jimmy Durante might say..............
I yam what I yam ............
In legal parlance you are who you are so that would be Charley Married Name also known as Charley Maiden Name or the other way around.
Mind you, if chopping and changing from one name to the other, it does tend to cause a lot of confusion and there is a lot to be said for opting to be one or the other.
mf