Domain registrations are handled by domain registrants/registries to the exclusion of other authorities. These registrants are usually either an ISP or an ICANN-accredited domain name registrar. The technical processes for domain names are not explicitly covered by the law, but rather by the so-called Domain Name System (DNS) rules. Websites can be registered with any domain registrant under the .com/.net/.org/.info/.biz/.name/.mobi/.cc/. there are several other domain extensions (such as .ai/.io) and more are still being created.
The process for registering a domain is relatively easy, but there are many things to consider. One of the most important considerations is the availability of your desired domain name.
As such, make sure the domain you are looking for is available by typing it into a site like https://www.namecheap.com/. This will confirm whether or not the domain is available for registration or if it's already taken.