Changing the name of a *WSUS* server is handled by deleting the old registration, and then creating a new registration.
You'll find the "Update Services Registration Management" tool by selecting the "Update Services" node of the console, and then right click for the context menu, or use the Actions Pane on the right.
However, changing the name of the Patch Manager server is a bit more problematic, because the Patch Manager Primary Application Server (PAS) is a Certificate Authority for the entire Patch Manager infrastructure (including other PM servers and all consoles). The Root Certificate Authority and the Server Certificate are issued in the name of the server to which Patch Manager was installed.
You'll need to reprovision the certificates using the command-line setuphelper.exe utility which is found in %Program Files%\SolarWinds\Patch Manager\Server.
The specific option you'll need is:
Beyond that, update the DNS records to reflect the new hostname and old IP Address, and then disconnect/reconnect the console sessions. The console session will download and install the new certificate.
(You can delete the old certificates from the certificate stores, if you wish.)
Finally, you may also wish to access the dbo.devices and dbo.ewdgs tables in the database and delete the references to the old servername.