Since neither smith.name nor the wildcard *.name appear in the Public Suffix List (https://publicsuffix.org/), browsers would likely allow any page on a *.smith.name domain to set cookies for .smith.name.
There was an effort to properly handle the .name 2LDs, but it was never resolved because there’s no easy way to tell a reserved 2LD (open for 3LD registrations only) apart from a normal 2LD on .name: https://github.com/publicsuffix/list/issues/2306
So yes, this TLD’s setup is in fact pretty insane.
> no easy way to tell a reserved 2LD (open for 3LD registrations only) apart from a normal 2LD on .name
And that's one reason why the public-ness of a hierarchy level belongs on a DNS record on that level and not some separately-distributed side list.
I'm always mystified why we haven't leveraged DNS.
I mean: why not have cookie policy set by a flag in DNS? Not unlike DKIM or even SSHFP.
Of course, we wouldn't need the entire certificate industry if we simply looked up a site's PK along with its DNS record...
I think this says more about how the cookies security model is stupid. They should always have been scoped to the single, exact name they were set from and nothing else. Websites would have had to be designed a bit more thoughtfully.