Since there has been no official catalog of the eddies currently present in the game, we should probably make our own. Post which eddies you have that are not previously listed on this thread and lets see if we can identify all possible character drops.
I have:
Eddie
Wickerman Eddie
Speed of Light Eddie
Mummy Eddie
Gunner eddie

I know of a few others already present but do not have them personally:
Aces High Eddie, Carriage Rider eddie, Pharaoh eddie, Rainmaker eddie, Vampire hunter eddie, samurai eddie, Tailgunner eddie, cyborg eddie and visions eddie.

Lets see what others are present int he game.