How do I register an arbitrary domain?

Here are two ways to register any domain (including TLD) for any IP address in your managed environment:

For example, 127.0.0.1example.stackoverflow in /etc/hosts will resolve the name to 127.0.0.1 by requesting from the browser or from the curl to the URL example.stackoverflow.

However, this should be done on a per-terminal basis, and if you want multiple machines to have the same access, you might want to set up the DNS server below.
In addition, /etc/hosts is the configuration in Unix-like OS and appears to be equivalent to the file C:\Windows\System32\drivers\etc\hosts on Windows.

You can also perform name resolution by configuring the DNS server to correspond to the IP address and the domain you want to specify, and by configuring the DNS server that you created on each machine.It appears that you can configure it from the registry /etc/resolve.conf for Unix-based OSes and HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Tcpip\Parameters for Windows.

Examples of DNS servers include BIND, which has a long history, and CoreDNS, which has been actively developed in recent years.

Bitnet launched the world's first World Wide Web (WWW) site in 1991.by Bernard Lee of CERN), which was in operation in 1981.
Bitnet started as a system to connect university computers in the days when there was no WWW yet.At that time, there was no organization, such as IPNIC, that managed the IP domain, and there was no IETF.There was no IP domain management mechanism in itself.
Later, IP domain management and so on came into being close to a "pseudo-top-level domain" in considering what the old BITNET would now be.

If you want to give a name that you like, come up with something that doesn't exist in the world at this time (which doesn't exist in anyone's thoughts).Then you can name it whatever you want.