Your name confusion is missing the point. It's the central registration done at a national level, not a True delimitation of which domain names which companies can own. A company could use downloadfreeram.tk, as long as it's officially registered in the national company register.
OK. What do you do in the United States where every state (and territory and the federal administrative district) has its own company register? Or where a vast number of businesses are sole proprietorships that have registered their trade name in their local county office?