When .name was new, you may have needed to contract with the registry directly, it was an early new gTLD and I don't remember if they started with the registry/registrar split or not.
Afaik, new registrants are not able to register a third level domain, but second level domains have been available for a long time.
It's just a combination in the ambiguity of what "it discards the dot" should mean in GGP's message combined with the article already clarifying 3rd level domains are not available on .name anymore leading to a lot of confused comments.
"Although they will be closing new registrations for 3rd-level .name domains, all existing domains (including this website) and email redirects will remain indefinitely."
They were apparently planning on shutting down the whole TLD. They will be leaving it up for existing registrants, but not allowing new registrations.
So the weird part then comes in: are all second level domains that have third level registrations now reserved? Do they stop being reserved if the last third level registration expires without being renewed?
Yes, second level domains that overlap with a registered third level domain have never been available. Under the original proposal, once all the third level domains were dropped, the overlapping second level domains would have been available (first come, first served). I believe current practice is the second level domain becomes available if all of the third level domains expire. Registrants in other threads indicated that there's no process to have an orderly transition from being the only the registrant of a third level domain under a specific second level name to registering that second level domain ... you would have to let your current name expire and hope to catch the second level name.
It was initially! But there was enough demand for second-level registrations that they opened that up too (and set the stage for this whole mess).