One feature of running your own server is that you are responsible for keeping it
There are hundreds of companies who will sell you a domain, at a price. Depending on the company and the domain you want to buy that price can range from (in theory at least) free to thousands of dollars a year.
I used to recommend freenom.com which purports to offer free domains but I failed the last couple of times I tried getting a free domain from them recently. The failure was right at the end of the process which was frustrating. It is not impossible that they will sell you a domain for cheap if not for free but I haven't bothered to try, they certainly advertise that they will sell you them.
No matter, do a search for domains you like from places that are cheap. namecheap.com is exactly what it says on the tin, for example. Just don't fall for their attempts to sell you anything other than the name. A couple of domain sellers that seem willing to stand up for free speech are Epik and Porkbun (the latter certainly seems to offer cheap rates for a wide variety of domains) but I make no specific recomendation for either of these or namecheap.
You can also look at some of the more obscure country code TLDs and buy direct from them (this blog is hosted on a .st domain for example and I also have a .nu domain) or, if paranoid, look for domain registrars in places like Sweden or Switzerland which are less likely to roll over when a twitter mob comes after you.
Things to think about when choosing a domain include how easy it will be for people to type and remember it as well as whether it helps describe what you want to use it for.
I personally tend to go for short names, so I'd tend to pick short.name over longdescriptivename.com but that's a matter of choice. You may also find it advantageous to not have a domain name that identifies you to the level that lets people dox you (smith.com is less identifiable than fredsmith.com which in turn is less identifiable than fsmith-dallas.com), although that does of course heavily depend on the reason why you want your micronetia site.
For the micronetia project you are, initially at least, likely to just use one hostname within the domain (e.g. blog.example.com) but having an entire domain of your own means that you can later setup subdomains like home.example.com, roaming.example.com or perhaps one for each child in a family.
No matter what, buy a domain and don't plan to share it with others you don't trust with everything.
Finally when you have bought it, do not set nameservers or anything else unless you absolutely must bcause they are going to be changed really quickly. If you have to set things up use a dummy IP address like 126.96.36.199 or your current IP address for whatever you have to set up. The only exception to this is that if you want to tie your domain to your current email provider (especially if it's someone like protonmail) you might as well follow the instructions to do that because you can then use email addresses like "[email protected]" to register with cloudflare instead of using a protonmail or gmail address.