I actually remember seeing a Trainer with my name, but there's a specific reason why. This was before they raised the character cap, so I couldn't use my name for my Trainer. When I went around fighting NPCs, lo and behold, one of them had my name crammed in there in skinny letters, despite my being unable to use it myself.
I'm picturing it as a-yep, had to be this little twit Lass with a Budew. It can't have been any other game. This was my first game, one of the first routes. . .darn, the resentment must be BURNED in there. XD