but which support the actual third-level domains? for example, my last name is already taken as a .name domain by verisign, what if i want my firstname.lastname.name domain?
The third-level domains are still being discontinued, it’s just that people who already have one get to keep it.
You'd have to try to find the contact that owns lastname.name and work out a private deal - you won't get ICANN protections though.
One can't (officially) register such 3rd level domains anywhere anymore.
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.