What’s in a Name?

I have often wondered why it is that in spite of the woman being the one to actually bear a child in her womb for 9 months and then giving birth to her child enduring the pain, she rarely gets to claim ownership of the child.
By ownership, I don’t mean the physical ownership. That obviously is hers. For the next three years at least, the whole family is just too happy to let her take the burden of the late nights and diaper changes and the milk and everything else that automatically becomes her responsibility.
But the day he/she is born, the proud father automatically attaches him name to the child’s name. It’s the same in every part of the world. At least I think so. Why? Just out of sheer curiosity. Why?
If the child is a girl, she can’t live with her maiden name for long. After marriage she is expected to change it again to match her husband’s.
Is it mandatory that the names have to change? Is it mandatory that we have to use the father’s name as the surname? What’s wrong with using the mother’s name?
To all those feminists who claim to fight for the equality of women, I have a sincere request. Change this fundamental rule. This rule is the one that automatically gives the man the all-powerful position in a household.
Times no longer confine the woman to the home. She can chose to work outside the home, from her home, or chose to do whatever she wants to with her life. No law prevents her from living her life as per her wishes. No law prevents her from wanting to live a single life either. No law forces women/men to be married. And certainly no law states that they have to have children.
The choices are many. But yet we succumb to the rules laid down by our parents and our society. We claim to live a modern life and yet still live in the shade of the Old World.
What do you think?
P.S: I am strictly speaking about the educated middle and upper classes here. The plight of the women in villages is still what it used to be years ago.