The domain password and the one you configure in Agent Explorer are one and the same. If you change it in Agent Explorer, it is changed in AD. If the supervisor changes it on a domain PC/Server, there is no need to do anything in Agent Explorer. The only thing I sometimes do within AD is set the password to never expire (want to okay it with your security folks obviously). That prevents a supervisor from being locked out after a while if they only use their login for Webview or Reskilling and never actually log into a domain machine.
I have never tried modifying the actual username. Since it's grayed out, you'll probably need to delete/recreate. Short of doing that, you could try un-checking the Supervisor Agent box, saving the agent, then Retrieving again to see if that enables you to start over with the supervisor portion.