When a Fediverse server is created, you have to give it its own name. This can be a domain name (example.com) or subdomain (social.example.com). People can use this server name when signing into their account on an app, or when using the server through a web browser.
The best domain names are usually short, easy to spell and memorable. You may want to avoid offensive words, as they can make it difficult to tell people about your server on other platforms. If you already own a domain, you can use subdomains for your servers.
It’s also probably a good idea to use a name that doesn’t mention the software that it is running. For example, if you were making a Mastodon server you probably shouldn’t mention the word Mastodon in the domain or subdomain. Software projects tend to change over the years, in their content, leadership or maintenance, and it may be that in the future you want to switch to a different kind of software on your server. It could be confusing for your users if your server mentions one kind of software but runs another. Alternatively, software projects sometimes rename themselves, and this too can cause confusion for your server’s users. On top of this, some software projects trademark their names and only let servers use the name if they’re running that specific software. This could make it legally difficult for your server to transition to another kind of software in the future.