Hi,
You can configure the network category on a Server Core machine with the following method.
The network location description is stored in the following registry value:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\NetworkList\Profiles\{<Network GUID>}
The value of Category is set as follows;
Public = 0
Home = 1
Work = 2
In this way, you can assign the network category by modifying the value of Category as below.
Hope this helps.