So let us begin!
Bulbasaur line: Buddy
Buds on plants are flowers that are about to bloom.
What? This isn't very creative? Well, they can't all be winners.
Charmander line: Char
Believe it or not, it's actually a name. Named for Char Aznable, a famous pilot from Gundam. And, well, the term "char" when referring to burns. In fact, in the Pokémon card game, the Burn status was referred to as "Char."
Squirtle line: Rockbottom
Bloody image wouldn't work...
Named for a living MacGuffin from the Redwall novel Rakkety Tam. Known to his wolverine keepers as the Walking Stone, Rockbottom was a sign of rulership in the Land of Ice and Snow.
Caterpie line: Carle
Named for a famous children's book author, whose works include The Very Hungry Caterpillar.
Weedle line: Gurren
Named for half of the titular mecha of Tengen Toppa Gurren Lagann. Gurren is everything below Gurren Lagann's neck. The show's constant use of drills as symbolism is well-known, and will be seen multiple times in these names.
Pidgey line: Valiant
Named for Disney's Valiant, an animated film about carrier pigeons in WWII. Or WWI. I forget exactly when the movie takes place.
Fun fact: Some carrier pigeons actually received high honors for heroism during various wars.
Rattata line: Cluny
Named for the first and greatest villain in the late Brian Jacques' fantasy series of novels, Redwall. Cluny is a one-eyed rat with a long, whiplike tail and many resemblances to Satan.
Due to Redwall's nature as a mouse world, and the fact that it's my absolute favorite series of literature, expect to see a LOT of it in the nicknames.
Spearow line: Warbeak
Oh look, more Redwall right away. Named for the sparrow queen in the original Redwall. Like all sparrows, Warbeak was a berserk warrior with a fiery disposition and a fierce devotion to her friends.
Ekans line: Ydersius
Named for the chaotic evil god of the serpentfolk in the Pathfinder RPG campaign setting. Ydersius is a god in a state of limbo: He's still technically alive, but his skull is entombed in a pit of magma, while his headless torso blindly stumbles through the Darklands.
Pikachu line: Bumblebee
Named for a recurring character from the Transformers franchise. Let's face it; Pikachu was designed to fill the same purpose as Bumblebee: MOICHANDISING! MOICHANDISING!
Sandshrew line: Log-a-Log
A title given to shrew chieftains in the Redwall series.
More to come later, it took long enough to put this together.
