I'll give some shared names....
  1. Tom Cruise or Tom (Thomas) Paine.
    Total common sense.
  2. Bill Clinton or Bill Pullman.
    They've both done a lot for society. Are we worrying about international affairs before our own too much? Bill Pullman. Do we want to give it to a Nobel-Prize-Man-of-the-Year Sort? Hmmmm... I think it would have to be the former.
  3. Mary Mary Quite Contrary or Bloody Mary
    Both quite contrary. One killed in her contradictory efforts. One did not and wasn't real. I'm going for Contrary.
  4. Ice-T or Ice-Cube
    SVU = Ice-T. Nuff said.
  5. Andy Richter or Andy (Andrew) Jackson
    I'm always pushing for the funny guy. But if someone said to you they were giving you a whole bunch of pieces of paper with Andy Jackson's (can I call him Andy?) pic. on them, and the same for Andy Richter, I'd go for the Jacksons until I knew that Richter was on legal paper tender.
  6. Sally Ride or Sally Field
    First woman, space, pioneer, NASA vs. actress, legendary, pioneer, SAG. Oy. It's a draw.
  7. Morgan Freeman or Morgan Fairchild
  8. Paris Hilton or Count Paris from Romeo and Juliet
    Suggested by @ChrisK
  9. Doc Holliday and Doc (Emmett) Brown
    Suggested by @ChrisK