That's arbitrary.fixed, which is something also slightly different.

I know this sounds absolutely absurd and your mind must be screaming "so just get arbitrary.fixed and assign yourself whatever.aribtrary.fixed?" at you... but stick with me and I can say with, dare I say, 61% confidence what .name was doing will make you think "uh - ok, yeah... I... guess. People did that?" :).

If you own smith.uk then great - you can be john.smith.uk. What about Jim Smith in the UK? Is he supposed to just reach out to John Smith and ask for jim.smith.uk to be delegated to him? What about the thousands of other (anything but John) Smiths, are they just supposed to pester John and ask if he'll delegate the name? What if Jane Doe doesn't want to delegate to other Does? What if Bob Johnson does and then dies - lapsing the renewal? It's all a big mess because one person is assigned arbitrary.tld.

That's where arbitrary.arbitrary.tld comes in - arbitrary.tld is managed by the same ones running tld. Now thousands of different people can get their john.smith.tld and jim.smith.tld without having to worry about who controls smith.tld any more. Now sure, there is more than one John Smith... but the chance an individual is able to register their name goes from 1/last to 1/(first*last) and the even when your name is taken it'll take fewer extra characters/nicname variations to find an open one close to it (like jim2.smith.name or jimmy.smith.name).

That's what .name was and why tlds like .uk or third level zones under them like .co.uk aren't really the same thing. The 2nd level isn't both arbitrary AND controlled by the tld operator at the same time. The closest you could get in a normal .tld is to start a service which tries to buy up every lastname.tld, but it's not really practical to try to do so and you'll always end up with someone who doesn't want to sell or some name you didn't think to buy.