I tend to name my Playable Characters rather random names. Sometimes I develop them into characters.
The ones I can very clearly remember start at Gen 3 because honestly it's been too long since I've effed around with Gen 1 and 2. xD I'm pretty sure I had a Kenta in one of the Gen 2 games though. because the Raikou Special was awesome.
Ruby and Sapphire: I apparently used Mieu in a Japanese rom-run of Sapphire (Phantasy Star 3 reference) and April in a rom-run of Ruby. The prototype Cori also happened on a Sapphire rom, but more on that later.
Emerald: Over the years I've amassed three playthroughs of Emerald featuring three names and teams that became actual characters of mine. They were Cori (because I rather like that name), Soleil (because it fit the way she looked like in my mind and also means 'sun', which is appropriate considering her starter was a fire-type) and Deryn (whose name means 'bird', which is fitting considering I created her on board a flying airplane).
LeafGreen: Amelie. For no real reason except that I liked the sound of it.
Diamond: my ACTUAL copy of Diamond's player character is named Colin, which is one of my favorite male names. In the few rom-runs I've done I've used the names JeanLuc and Picard. Because look at the guy. He wears a frigging beret.
Platinum: Continuing on the French theme, my Platinum rom-run character was named Valjean. XD
SoulSilver: Erol, another favorite male name of mine.
I'm not sure what I'll use for the English version of White, though I named the character Jaden in both the Japanese Black and white Roms, because LOOK at him. He's such a damnable Jaden Yuki clone.