Change of insurance

Hello people, have a little question about how to change. So current situation: my mother is a holder and I am an insurance holder. the car is registered in circle a by my mother. now I want to switch to another insurance, which is significantly cheaper if I am a holder and an insurance holder. so I have to register it to the circle in which I live so circle b! where do I have to go now and what do I have to report everything. P.S. the car should if possible always be ready to drive so it wants to log off somewhere completely so that I can drive for the first time even net… hope you understand me… number plates I must therefore also make mandatory, since other circle (b)?!!! thank you for your help