There is no one central place for name registrations – there are several. Network Solutions is one, Go-Daddy is another. These are only two examples, but are probably the two largest registrars.
Once the name is registered, it must be resolved via DNS (Distributed Name Services). Here again, someone must host your name. And again, the above two companies will do it for you, or your service provider can.
For DNS, there is – in effect – one central place – because the top level domains (like .com, .biz, .org) each have a “well known” fixed IP address where to start. These are usually served by multiple computers residing at one address (load sharing), but as far as your system is concerned, it only needs to know how to get to the root to start the search.
In practice, your computer does not start with the root ro resolve a name – instead it goes to your internet service provider’s DNS server. These ISP DNS servers will cache many popular name / address translations – and then will go to the root servers only as required to resolve a new name, or every so often to verify a cached name. In this way, the root servers are not overloaded as each query comes along.