Multiplayer, a key aspect of Pokémon. Using the DS's multiple techniques, there are many schemes for battling and getting friends. Union Room, WiFi Connection. It's all possible. However, so you can differenciate the people you're battling, especially in the Union Room and your Friend Roster in the Pal Pad, the game allows for you to have an avatar. In past games, these avatars were determined solely on Trainer ID. It is the same here, but with a twist
If you go to Oreburgh City and talk to the trainer in the Pokémon Center shown here, he will give you options for Trainers to change your persona to. Once selected, this persona will appear on your Friend's Roster when you next connect to them and will be your sprite within the union room for your friends as well. However you are only given four choices. There are 8 sets per gender. This is what is determined by your Trainer ID. We will create a calculator of sorts at a later date, but below are the lists of trainers in Alphabetical order;

Male

Ace Trainer Black Belt Psychic School Kid
Ace Trainer Black Belt Rough Neck Ruin Maniac
Ace Trainer Bug Catcher Psychic Ruin Maniac
Ace Trainer Bug Catcher Rough Neck School Kid
Black Belt Psychic Rich Boy Ruin Maniac
Black Belt Rich Boy Rough Neck School Kid
Bug Catcher Psychic Rich Boy School Kid
Bug Catcher Rich Boy Rough Neck Ruin Maniac

Female

Ace Trainer Battle Girl Beauty Lass
Ace Trainer Battle Girl Cowgirl Idol
Ace Trainer Beauty Idol Socialite
Ace Trainer Cowgirl Lass Socialite
Battle Girl Beauty Idol Lady
Battle Girl Beauty Lady Lass
Beauty Lady Lass Socialite
Cowgirl Idol Lady Socialite

There you have it. Once you have selected the four Trainers from which you are given the choice, your Trainer Identity will be placed on your friend's Pal Pads in the next time you battle them.