I need to take a running windows desktop box that's part of a domain, give it a new computer name, and then continue working on it (with the box having the new name), without having to reboot at ...

Windows finally includes a tool to manage local admin passwords, but admins will still need to do some work to make it useful.

Actually you only need to install the root CA certificate on the non-domain joined machined so that they trust the certificate on the RDP server. You can do that pretty easily via PowerShell.