As a woman, you have the right to choose
Does the baby not have two parents then
Yes, but legally if the parents are unmarried it's the mother who has to be there to register the child (which includes choosing the surname). So as a woman (who is not married to her child's father) she does have the right to choose. That doesn't mean that the surname shouldn't, in practice, be agreed between both parents -- but in law it's up to the mother (unless the parents are married, in which case it's up to whichever parent can get to the register office first).