In Mario Superstar Baseball, every captain has four possible team names and logos: one default, one when most of the team members match the captain's type, and two special ones only used when the team includes four particular players. Below are all logos with their requirements.
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Yes they do (sorry if you've already looked into this yourself by now).
spriters-resource.com/gamecube/mario
Birdo and Bowser got the usual localization changes, but there are some differences (Peach Dynasties were Peach Valkyries, Luigi Harmonies became Luigi vacuums).
Poor Waluigi though.