The Remote Desktop Session through RDP has a different TeamViewer ID than the standard service running.
When you tell the server to remote reboot it gives you the prompt that “Multi User View Mode is enabled” and that logging on again will require you to log in with the new ID XXX XXX XXX.
To connect to the correct ID note it down and then cancel the remote reboot.
Once that is finished you can log out of the RDP and then log in with the new TeamViewer ID.
This will be your permanent ID outside of the RDP Scope.