at the moment, claiming is realized on first arrived, first served.
My understanding is the following , please someone correct me if I’m off :
say I create coolsite.bzz
then another guy has the same idea, and tries to create it again. Unfortunately for them, the hash of “coolsite.bzz” already translates to an adress of owned data in the XOR space, and the network will refuse to create that name again.
When I point my browser to “coolsite.bzz”, the request is translated in xor space adressing, and the network hands the corresponding data to my browser.
Later, it is expected that you will have to pay some safecoin to be able to register such a name.
Regarding the unicity / non-unicity of vanity names, there have been nice discussions on the theme, including about pet naming system, which I really like :