This should never be necessary. It will require you to not only re-claim the server into the new account, but also to log out each and every client from the old and into the new account.
If you want to carry forward anyway with this, you need to remove the former account from the Windows registry, followed by claiming the server into the new account.
Don’t forget to stop Plex server using its task tray icon before proceeding.
See You need to reclaim your server, but don't dare to touch the Windows Registry
on how to remove the former account.
Then follow New Claiming Requirement for Windows to reclaim the server.
