Once a domain name is registered, it belongs to the person or company that registered it. If you are really interested in having a domain name that is already registered to someone else, you can contact the owner of the domain name to find out if the name is for sale or you can wait for the registration to expire.
Domain owners are registered in the Internet Corporation for Assigned Names and Numbers (ICANN) database, which you can search using a service called WHOIS.
