It appears to be some setup configuration on the new one to where the Select Computer browse dialog does not find the host name but instead only returns the FQDN which is how you see it listed in Hyper-V manager.
Some ideas here with that one
https://serverfault.com/questions/44030/local-dns-not-resolving-host-name-but-will-resolve-fqdn
but getting off in the weeds here. You could close up this one here and start a new thread to discuss this new problem. Please don't forget to close up the thread here by marking answer if the reply is helpful--