No need to have an external domain. And you can set up an internal DNS to route any domain name to any IP address. Just be sure not to point anything to your external IP address from your ISP or any globally addressable IPv6 addresses.

Issue is that it might confuse your devices that jump between internal access and external access like your phone if you use a domain name that’s owned by someone else, like example.com. I have two domains, one for my VPSs and one for internal stuff. So when my devices are outside the network they can’t resolve any of the DNS addresses that are set up inside and can’t access any of the IP addresses. That is unless I connect with vpn. I also have pangolin for a few things that are accessible externally, but that’s rare since apps can’t use those kinds of authentication systems, just web front ends.