In Russian this works both ways for grandparents and for parents. If a family has a tradition to name a boy after a grandfather then taking into account Russians' using patronymic the boy's and his grandfather's names would coincide totally as well as the names of the father and the grand-grandfather. On the other hand if a family like it is possible to name a boy after his father and we can take for example our newly elected old president "Владимир Владимирович".
According to what I read about Koreans these two cases are close to one another. A Korean name consist of three parts. First is the family name and the two other parts are the first name. The last part of the first name is shared among the siblings as a tradition.