There's no prohibition against naming a son after a living relative. However, it is the custom of Jews of European descent not to name children after living relatives. If they name the child after a relative, their custom is to name the child after a deceased relative, as if to say that this child will carry on their tradition.
The Jews of the Middle East, North Africa and Asia do name children after living relatives, and they consider it a great honor to have a child named for them. However, they too generally refrain from naming a child after a living parent. Usually grandparents are the first ones honored by having a child named for them.