The only time you can appear as a Trainer besides the generic Ruby one that you always are is if you mix records with someone, and you have a Secret Base. Then the person you mixed records with can battle you in their game, and you will appear as a different Trainer depending on your ID number:
You can't actually become one, I believe that you are talking about the Secret Base trainers. Once you have Mixed Records with a friend, all of the Secret Bases on their game will also be put on your game. Your game can store up to 10 secret bases. Inside the secret bases, you can battle your friends, they will have the same Pokémon as your friends did when you mixed records with them. However, their character is not the normal character. The type of trainer that they will show up as will be determined by their gender and the last digit of their trainer ID number. Here is a link explaining this more... http://serebii.net/pokemon_advance/base/trainer.shtml