What conditions are you imagining in which a donor is living but not aware of specifically who would be receiving the organ before agreeing? Tests need to be done to ensure compatibility, and a kidney is a lot to ask and probably wouldn't be agreed to unless it helps a loved one.
I feel like this is a strange premise whose goal is trying to try to move the line little by little until people are willing to say they're a little bit racist/sexist. Or until people are willing to admit they don't think others should have control over decisions made about their bodies. Be honest about your ends here instead of dreaming up fictions that make so little sense the answers are unproductive.