Her name is her heritage... you are depriving it of her true name...
I think that is going a bit far, or every woman, giving up her TRUE name after marrying would be forsaking her heritage.
I think a name is just that.
A couple of letters by which people can adress you, and distinguish between different people.
If your daughter will feel better having the same name as the rest of the family, as I can imagine she would, go ahead, and make her life easier.
Her dad should give her more than a name, if he is interested in being part of her life.