Changing WiFi changes the ID

You don’t have to do that. Currently you have to shut down the Pi, remove the SD and edit the existing file config/wireless. After saving, put the SD back in and start. Your Pi will try the new WiFi settings. See here for a description of that file: https://info-beamer.com/doc/device-configuration#wificonfiguration

In the next OS version this will be a lot easier as you can edit this kind of setting directly on the device page itself. If you want to try this out, follow this guide: Trying out the next info-beamer OS version before release

After switching to the ‘testing’ version of the OS, just reload the device page, go to the Device configuration section and click on Edit…. Then select the Networking tab, edit the configuration and click on Apply configuration and reboot device:

Let me know if that helps.