There is no need to change your toothpaste if you are not using medicated pastes.
If there are some antibacterial medicines in the paste, then after some time the bacteria in mouth may develop resistance to them, however if you are using simple paste there is no need to change it. I will also stress that the paste does not have much effect on brushing. It is the method of brushing which is important than the paste. You need to look into brushing technique more than the paste.