I am planning to build my own hosting for my website but I don't have much information about Domain Name Service(DNS), I know how it works but I do not know who is responsible, Whom does Hosting companies ask to register domain names?
This is a complicated and expensive process, that will certainly cost many thousands of dollars to complete.
It depends on which Top Level Domain you wish to register, but the first step will very likely be gaining ICANN registrar Accreditation
You will then most likely need financial and business verification.
Once you have gained registrar status, you would then need the technical expertise to maintain your records with the root servers.
In order to register a domain for a website, it will be infinitely cheaper, easier and quicker to go one of the bulk domain registars.