[tokai]

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.

[nocoiner]

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?

[TheOtherHobbes]

Sounds like there might be some kind of solution for this that - just spitballing here - uses networked computers.

[crote]

So private individuals would not be allowed to register domains?

It sounds a bit like you just want WHOIS, which in practice turned out to be a bit useless.