this depends on the country in which the baby was born, in my country is the father's name first, then the mother, but in Brazil for example, the first surname of the mother after the father, not a matter of feminism , is a matter of culture and understanding between couples, the final decision is of the parents.
In China, the baby always follow the surname fo his/her father. But nowadays this is not a definite case, because the family members are more open toward the issue and this would finally up to their negotiation.
:) I agree that the child takes mother's surname! I strongly suggest my elder sister to give birth to another child, so that the another child could have the surname of my sister.However, my brother in law doesn't agree with my idea. He is very chauvinism.