Start from the TLD lists. https://en.wikipedia.org/wiki/List_of_Internet_top-level_dom... led to https://en.wikipedia.org/wiki/.name led to https://www.verisign.com/domain-names/name-domains

Same as any gTLD, pick your favorite registrar and they probably support it. Give your registrar money, they'll give the registry money and boom. (more or less)

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.

Available under standard registrars that offer many TLDs, like inwx.com: https://www.inwx.com/en/domain/check?domain=testtest123.name...

Did you read the link?

"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.