You are not the trainer, you are the player, the trainer is the PC in the game, thus when pokemon are transferred they are not with the same trainer.
You do not share the same ID number in every game, and might not even share the same name.
It doesn't matter if the actual character is different in each game because let's be honest; each main playable character is the same silent-protagonist essentially. They might look different and come from different regions, but they share the same basic role. On top of this, you, the player, are the one who trains the Pokemon, not the in-game character. Ergo, the player is the trainer. If I train Pokemon in one game, and train Pokemon in another, logic dictates that since I am the trainer on both games, both games have the same trainer:
me. It's a Role-playing Game, so if I play as the trainer, I take that role.
I understand how it works, though: different ID number (although my name is the same in every game) = inable to nickname. This is what I want revoked as it is silly in my opinion. Sure, one could argue that it is out of respect of the previous trainer, but this lacks validity; that trainer gave the Pokemon to me, indicating that the trainer likely did not want it. Since it is mine, I
should have the ability to change it's name (especially if it is a name that completely does not fit e.g. a Rayquaza I got that was named 'He-Man'). The same argument lies with Pokemon Transporter - the Pokemon is mine, so I should have the ability to change it's name.