Nowadays I like to name my trainer after a character I created. My rival's name is more difficult... although in D/P/Pt I've also named them after characters I created.
Diamond
Trainer: Lupin
Rival: Diego
*This is the only Pokemon game I have where my trainer is a boy. I named him after my favourite character to use in RPG's. The rival is based off a Team Rocket member I created for a Pokemon fanfic long ago.
Pearl
Trainer: Yamiko
Rival: Gabe
*I got Diamond and Pearl at the same time, so I figured one trainer would be a boy and the other a girl. In what used to be my Pokemon fanfic, Yamiko and Lupin were a couple. As for the rival, Gabe was yet another Team Rocket member in that fanfic.
Platinum
Trainer: Eve
Rival: Warren
*I have no story characters named Eve, so I have no idea where that name came from. But Warren was one of the characters in my fanfic... he wasn't a villain, but he looked and acted very much like the D/P/Pt rival.