So I am trying to make a website when I start to look into getting a domain, I am going to run this on a server I have build and I realise that I have to rent a domain, so I put my wanted website name and it says that there is no connection or "DNS_PROBE_FINISHED_NXDOMAIN". So this means that no one has this domain, can I host this domain without buying it from somewhere?
"So this means that no one has this domain, can i host this domain without buying it from somewhere?"
No, at least if you want it to be reachable publicly from anywhere. Simple to see why: imagine if you choose a name for your website, and someone else also uses the same name. How would it work globally if nothing enforces uniqueness?
After that, technically, nothing forces you to pay for it (besides some specific TLDs offering domains under certain conditions, like
.tk). Imagine you have a friend already owning (and paying for)
example.com domain name. He can give you, for free,
xeneration.example.com (or any other name "under"
example.com for that matter), as long as you are happy with the "unfamiliar" format.
And of course locally, on your own network, you can define any names you want and use them. But noone else, outside of your network, will be able to use them without any specific setting.
I do not know much about domain names and any help would be apreciated
Did you try starting with the basics, aka Wikipedia:
You could then have a look at ICANN resources, ICANN being the non profit organization overseeing most of domain name related activities at least for the "registration" path (and some of their resources are translated in multiple languages):
Also if you do a search on this forum with "domain name" or "registration" or keywords like that I am sure you can find a lot of useful content, that you should review and then maybe ask for other more specific questions you may have.