You must use specialized services to register a domain name, which will be the address of your website on the Internet. 

You will have to check on the availability of the name you plan to use, and then register it with Internet authorities. There are fees associated with this process and it must be renewed annually. 
You can check our Web page on this question at

The domain name should always be registered in the name of the owner of the company for a business website to avoid risking loosing your domain name if your webmaster goes out of business and does not transfer the ownership back to his client. Always retain access and ownership of your domain name, and renew it upon when your initial subscription expires with THE SAME registrar company. 

Domain name registration information is public, so some companies send renewal notices to people who are not even their clients. This is a SCAM, since a domain name cannot be registered with a different company unless you ask your ISP to give you a transfer code. 
Make sure that you continue to do business with the same Registrar company, and in doubt, you can even check your own registration information by looking up on a 'Who is' database with your domain name. The name of the registrar company and expiration details will be listed.