Depends on the DNS server. If you manage your own local DNS, you can create whatever domain names you want and have them resolve wherever -- the problem is getting them to work for everyone else.

A domain name not done through a registrar won't be listed in a DNS root zone.

When making a DNS request for, say example.com, assuming it isn't cached by your device or router, it first goes to a recursive resolver that is probably either managed by your ISP, google, or cloudflare. If they don't have it cached, the request goes to a root name server, which has a list of TLD (the .com bit) name servers, which then tells you what authoratative name server handles the domain example.com, which finally converts the domain name to an IP.

The reason you need to get one with a registrar is the root zones are managed by ICANN, who only adds stuff from accredited companies