No, you cannot. The other trainers you see the back view for are a few trainers that tag along with you for certain events in certain parts of the game. The pretty green-haired girl, for instance, joins you in the forest, and leaves after a certain point, and the blue-hatted individual teams up with you at some point in the game, and later gives you a Riolu egg.
Following a few events in the game you can actually have these people re-join you at the battle tower.