I am raising a dark chao on Sonic Adventure 2:Battle, and I was wondering, can a chao change physically depending on which one of the three evil people train him? What I'm asking is if a chao raised the same way with Shadow, and a chao raised the same way with Eggman will be different.
They'd turn out the same. Only the character's side (Hero or Dark) affects the chao; the specific character doesn't make a difference in the chao's physical look. The chao will most likely become somewhat attached to whichever character you use most often, though.

~ Crazy C Lea