It depends on whose name their mother has put on the form when she registered the birth. If she hoped to get any sort of child support, she would put the father’s name, if she didn’t want anything to do with the father, she would put only her own surname when she registered the birth.
For the same reason that other children take their father’s last name. By the way — there are no illegitimate children — there are illegitimate parents, and a lot of arrogant people, though.
It’s the mother’s way of Compensating
If the child’s father is not going to be a part of the child’s life any other way, then they should at least have his last name
to avoid the appearance of illegitimacy, first off. then suppose the parents get married. the child will not have to go through adoption by his now legitimate father. also for child support purposes.