What should I do if I want to change the domain on which the JENTIS Tag Manager is active?

The best way to proceed is to create a new container for the new domain. Changing the domain in an existing container leads to a change in DNS Entry / A record , and this is as much work as the creation of a new container ist. If you create a new container for the new domain, you will be more mindful with the tailoring to the new domain. Just make sure to connect the JTM Elements such as the tools and the CMP Bridge in the way you did for the current container. 

Please note, that a container configuration CANNOT be copied onto a new container. You must reproduce container configurations manually.