If you want to set up a server, you will most likely need the following things:
This can be a shared hosting offer like VPS (virtual private server), which is a VM (virtual machine) running on the same physical server as other virtual machines, or a dedicated root server, which is a real machine, which you have all to yourself.
There are many domain registrars out there. Best is to find one, which is well known. You will probably need to create an account on the website of the domain registrar and log in to be able to check, whether you can get the desired domain from them, or whether that domain is already in use.
You need to come up with the actual domain name, which you hope to be able to register with the domain registrar.
You will need to find a hoster, which rents out servers to you. Typically the server will then be reachable via its IP address. Not idea for other people, if they need to remember the IP address of your server. That is why you probably want to get a domain as well.
Try to think of a simple yet original name, which likely is not yet used. To make approximately sure it is not yet used, try the following things:
If none of those yields proper results, it is likely, that your domain can still be bought.