I name mine after anime, game, and Disney characters, as well as foreign words that suit the Pokemon.
Zelda the Gardevoir-If you remember The Legend of Zelda: Ocarina of Time, you know that Zelda has psychic powers...and Gardevoir looks like a princess, so it makes sense.
Ariel the Vaporeon-Disney's famous mermaid (the reason I chose it), and the name of a fairy in Shakespeare's "The Tempest"
Luce the Ampharos-Italian for "light", since that's mainly what Ampharos do (give light) You say it Loo-chay, not Loose
Epona the Ponyta-Another Zelda reference, this time Link's horse, and the ancient Celtic goddess of horses.
Meeko the Linoone-after the raccoon from Disney's Pocahontas
Umi the Gyarados-Japanese for "sea"
Diddy the Chimchar-named for Diddy Kong
Erin the Lucario-feminized version of "Aaron", plus an ancient name for Ireland