Red blood cells, the primary component in transfusions, have no nucleus and no DNA. When blood is donated, it is processed in a number of ways but one important way is 'leukodepletion' - which is the removal of the white blood cells. If this wasn't done, the donated white blood cells would attack your body's tissues and cause inflammation.
A transfusion is supposed to give someone enough blood to last until they can make their own. So while it is theoretically possible to have other's white blood cells DNA in a sample, those cells will eventually be eliminated from the body.
A transfusion is supposed to give someone enough blood to last until they can make their own. So while it is theoretically possible to have other's white blood cells DNA in a sample, those cells will eventually be eliminated from the body.