The difference what I put as a) and what was written in the OP blog post are a couple of things.
1: In the blog post they wrote:
> this website vanishes in February. Despite the fact that it's registered and paid for until 2040.
So the way .name 3LDs worked, was that you had to pay for it. Not a free subdomain that’s handed out in return for the domain owner injecting ads into your site.
2: The other thing I meant by a) but that I failed to state explicitly is that in scenario a) I am imagining that doe.name and some other 2LDs with highly common last names had been bought by a third-party, similar to how the Freewebs company was owning freewebs.com and giving out subdomains of that to people. See also https://en.wikipedia.org/wiki/Webs_(web_hosting) for details on how Freewebs worked if interested and not familiar with them.
I would not have guessed that the .name registry itself was running a 3LD setup for everyone across all of .name, because it is so different from how all other TLD registries I know of manage the domain name hierarchies. For example .co.uk which is also 3LD was much more straightforward to understand and recognise historically because the 2nd level was a category (alongside a few other categories like .gov.uk, .ac.uk, .org.uk).
A few years ago, .uk opened to second level registration also, which somewhat similarly makes domains under .uk more confusing to me as someone outside the UK who knew about .co.uk and the likes because now I can no longer know if a 3LD under .uk is the way it is because it’s under an official category or not. For example, say that there is a 3LD domain manchester.autos.uk. I wouldn’t know if .autos.uk was an official category domain or not without specifically looking it up, now that 2LD registrations under .uk are open to others.