It's rare to receive whole blood. Usually you need packed RBCs if you're anemic (no DNA in RBCs), or fresh frozen plasma if need rapid correction of factor-related coagulopathy (no cells even), or platelet transfusion if thrombocytopenic (only megakaryocytes have DNA, not platelets). Receiving WBCs is not common, but in the case of whole blood transfusion, yes, for the lifespan of those WBCs, you would have someone else's DNA in your body. As for the bone marrow transplant comment... interesting... since you're receiving progenitor cells you could have someone else's DNA for a long long time. Good question.