Lots of people have interesting ideas when it comes to asking a player to sign their name. I've seen some people who collect only full name signatures, etc. Let's see some autographs that aren't "rare" in general but are rare to find.
Here's my Albert Belle, nee Joey Belle, signed rookie as Joey Belle with a "Tribe" inscription. If Albert is ever elected, as I firmly believe he should be, this card with this signature would be a grail to someone: