If a company has a name "x" is a name called "the x" ok?

you statement of facts is contradictory.  First you state that you own the domain to the"x".com but then you state that another company owns the domain "x".com. Which is correct.  If you want to have a domain and a company name that is the same, assuming that another company owns a domain that is the same as your preferred company name, you need to either buy the domain from the other company or choose a name that is available both as a company name and as a domain; while the mere ownership of a domain by another would not necessarily preclude you from using the name as a company name, it might place restrictions on your use of the name, especially if the name is also used by the other company as a trademark.  I think you need to discuss specific detailed facts with a trademark attorney before making any final decisions.