In my opinion, children should take both parents’ surnames because you are part of your father and of your mother too.
Why is it in some countries there is only father’s surname?
As I see, having only your father’s name or when you are married, your husband’s name is a very sexist measure. We are in the 21st century and the equality is an ethical value but in this case, it isn’t applied.
I live in Spain and all the children have both surnames and also women keep their own surnames when they get married. Other countries ought to learn this intelligent measure to making more obvious the sex equality.