>Now I am trying your suggestions on a Windows 10 Pro PC. Installed all components and can run a test.aspx.
>
>1. The result of nslookup dell2020:
>Server: Linksys11447 (I think this is my router) && Yes
>Address: 192.168.1.1 (I think this is the address the router assigns to this Windows 10 PC) && No, it's the router's LAN IPv4 address
>*** Linksys11447 can't find dell2020: Non-exisent domain.
>
>2. As I said above, the test with localhost works.
>
>3. When I replace the localhost with the computer name (dell2020) http://dell2020:8080/test.aspx
>I get message:
>dell2020's server IP address could not be found.
>
>What do you think is missing on this Windows 10 in order to set DNS to recognize the computer name, Dell2020?
>
>UPDATE:
>On this site I disabled Anonymous Authentication and enabled Windows Authentication. The test.aspx with localhost correctly returns IsAuthenticated True. And the test.aspx page shows that (Dmitry, me) is logged in.
>Everything correct.
>Then I did ipconfig and see that the IPv4 is 192.168.1.141. So I replaced the localhost with 192.168.1.141.
>Now, when I try to browse to test.aspx I am prompted, by Windows Security, to login using User Name and Password. Even though I (Dmitry) am the admin on this PC.
>Pretty much the same that I was getting on the customer VM server. When browsing to the test.aspx page using the server name, the access not allowed unless user enters User Name and Password.

In a typical home network, host (computer) names aren't added to local DNS by default, so they're not resolvable. For testing purposes usually the simplest thing is to modify Windows' HOSTS file: https://support.rackspace.com/how-to/modify-your-hosts-file/ . Your computer probably uses DHCP to get its LAN IPv4 address. If after a restart it gets a different address, you will need to update your HOSTS file. You can avoid this issue by switching your computer to a static IP address, either configured within Windows, or (more elegantly) via a DHCP reservation in your router. The latter always hands out the same IPv4 address to your computer when your computer asks for one.

As for differing results when using IP addresses in the URL: I suggest keeping your eye on the ball, and testing only those scenarios which will be used by your customer. Others may be of academic interest but are a hindrance in getting things done.