Women will never have social equality while, on marriage, their identity is subsumed into that of the man. Not only does the changing of her name to his indicate ownership (its original purpose), but pre-marriage friends who knew her only by her own name are left to wonder: who is she now?
They have no chance of finding her in a phone book or on Facebook, of meeting up again.
A man goes though life by the same name. He never suffers such sense of disappearance.
Identity inequality is a subtle, but strongly discriminatory tradition. Women will never achieve equality of respect until they achieve this equality of social status.