The mother and daughter must be blood related. So, did the boy come with a remarrying father? By his looks alone, the the boy could also be biologically related to the mother, but has a different father from the sister, but since the girl is called a step-sister, that shouldn't be the case.
In any case, even the girl took the new family name. I guess it makes sense if she's a warm sister. Although not knowing Japanese laws, maybe there wasn't even a choice.