Yes, that will work in both cases. The Server Name configured on the user side in the License Management Tool is the only parameter used by the licensing client to find the licensing server. If you install SelectServer on a new machine with the same name as the old server (of course you will need to shut down the old machine as you cannot have duplicate hostnames on the same network) and the new server will be findable in the DNS - the user machines will automatically get the licenses from the new server.
If you install SelectServer on a machine named differently and create an alias entry on the DNS server which will relate the old hostname (configured on user PCs) to the hostname of the new SelectServer - it will as well work fine.
