How do you claim it?

The nostr verification is essentially linking your pubkey to a site that either verifies your identity somewhat (you control both the pubkey and Twitter) or doxxs you at least partially (by linking your pubkey to a site you control-like a GitHub pages. Is that a decent understanding of the NIP?

U must be dreaming of an other net, there is no verification, anyone can use any 05 name in nostr, just dns sites responding, for a name with a pub, only ur pub is uniqe. The only thing a nip05 attests, is that a domain has a pub that match a name, the name itself is unprotecable from double assin...

It’s clearly you. What more do people want? Birth certificate + DNA samples?