Mine's always different, and it doesn't really follow a pattern though I do tend to pick short names.
Emerald- May, for the default name, and then Keri on a replay because I thought it was pretty.
Fire Red- Meg, a favorite character I've created, and then Orange because I was on a Pokémon Special kick and was thinking about Red and Yellow.
Diamond- Lily, for no good reason.
Platinum- Mitsumi, for the character using the Dawn design in another Pokémon manga.
HeartGold- Kiri at first, and then Ethan, the default. He was my first time playing as a guy, which felt kind of odd especially because his team was really cutesy.
Black- Yuki, for the new seasons mechanic (falling snow.)
Y- Jin, because I was thinking of an 'ice prince' character of that name who looked very much like the blond and blue eyed male default.
Omega Ruby- Haruka, because I wanted to pay homage to my first ever game where I was May without reusing the name, so I chose her Japanese name.