Well, when I named my character a few months back, I didn't really realize that I'd probably have to explain the name to my online friends I'd be playing with, and I didn't really think about it untill I had a battle with Alex. I named my character RQVHUL, which directly translated, doesn't mean a thing, however the Q is meant to be the letter ø, which I wasn't able to choose, in which case it'd be translated to ***hole. The story behind that was from a kind of a running gag between me and my friend, when he decided to play Sapphire. He'd never really played through a Pokemon game before, and the only reason he chose to was because he found out how much of a fan I was of the franchise. In the beginning he didn't take it seriously though, because he was in the mindset of so many others, being certain that Pokemon was only for little kids, and thus wasn't serious in naming the character. And thus, RQVHUL was created, which would turn out to be the name I would use in any other Pokemon game. He started having fun with the game and started taking it more seriously, and for some reason, and we just started liking the name for some reason. We pronounced it the way it was spelled though, so it never actually felt like the word it was supposed to be, which may be why we liked it lol. But yeah, that's the story of my characters' name.
I named the rival Kevin, which is the name of a really annoying guy that lives here in the town. For some reason, he always wanted to hang out with me, which wasn't really mutual. It came to a point where, whenever someone knocked on the door, I'd always have to check who it was before I went to open the door, which was hard to be subtle about, since there's a window on the door :( Eventually he stopped coming over all the time, and I was once again free \o/ But yeah, that's the reason I chose that name for my rival :D
As for my Pokemon, I chose either not to name them, unless I had a perfect name for them, if it was a Pokemon which either resembled someone here from PC or was one that they really liked, or whatever name the friend I mentioned earlier could lash out whenever he was over :p