However, only Mr. Mime and Mime Jr. really have two-worded names.
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On every Pokemon game, there is a name changer. He will allow you to change your Pokemon's name, either with a small fee, or free of charge.
You Can Go By The Pokemon Name Rater
Pokemon 2000
If you receive a Pokemon from a friend or from the Global Trading System, you cannot change it's name. The only way to make sure the Pokemon has a name that you like is to get it from a friend and ask the friend to change the Pokemon's name before they trade it to you. You can also trade Pokemon from one of your own games to another of your games, so the Pokemon will have a name that you chose.