The issue had nothing to do with the Windows Firewall. I had both "Network Discovery" and "File and Printer Sharing" enabled. I also disabled the Windows Firewall to see whether it made any difference. Eventually, I discovered the issue originated from hardware. The laptop allows both Ethernet and Wi-Fi connections to be simultaneously on. The Windows 10 Host name got registered under Wi-Fi and the MAC ID got registered under Ethernet. Both the computers I was having the issue on and the external test computer I was using were connected to the Ethernet network. There didn't seem to be any way for someone with a normal user account to remove entries from the connection tables for Ethernet and WiFi which basically enhances DNS.
I corrected the issue by doing 2 things: 1) Reconfiguring the device to allow Wi-Fi only when EtherNet is not used. 2) Changing the Window 10 Host name to allow the ISP's cable modem to recognize a new host name to add to the Ethernet connection.
Now I discovered a new issue which I'll need to take elsewhere since it doesn't appear to involve Windows. Both Ethernet and WiFi networks are on the same subnet 10.0.0.x. But devices on the WiFi network do not see the presence of devices with File and Printer Sharing on the Ethernet network. I wonder whether DNS is being enhanced by separate tables on the WiFi and Ethernet networks.