If you transfer your Pokemon from one game to another, like let's say from Soul Silver to Black 2, will the Pokemon that were transferred be yours in the Black 2 game or the other games Pokemon? I'm asking this because I have a different name in my Soul Silver game than in my Black 2 game.
No. Pokemon "ownership" is based on both the trainer's name and the original trainer ID which is a random 5-digit number (assigned when you start your game). Both values can be seen in a Pokemon's summary screen.
So even with the same name, the chance of having the same ID Number is extremely small.