Can't anyone set up a "registrar" for a subdomain of a domain they already use? They control the DNS record, right? Why is ICANN even involved here?
I don't see how this is any different, other than the second-level domain owner delegates their registrar job to the first-level domain owner.
There is something weird though if you control smith.name, that you don't control john.smith.name. The DNS system does convey some indirect concept of responsibility.
You can register both second (example.name) and third (first.last.name) level .name domains. However, once a third level name is registered, they reserve the parent second level domain.
ICANN is involved because Verisign is the registry operator for .name, and the contract between ICANN and Verisign gives ICANN some oversight power over Verisign's registry services. This includes some fairly limited oversight power over what they call "voluntary services", which are services that the registry provides that are not required to be provided by the contract. Apparently the registration of 3rd level domains and the email forwarding service are voluntary services, not services that Verisign is obligated to offer by the contract.