Have a look at handshake protocol. There's no authority there. And it's quite an original approach.

Petname systems are fine, they have their use, but when you want to make a billboard with your name, it's better to have a global unique resolution to that name, because you don't have control over everyone's web of trust. For someone with infinite fiat resources it's easy to register that name in thousands of other webs of trust, so you will be impersonated easily.
And resolving a naming conflict - if both candidates want that name - inevitably comes with a need for authority (community leader) who decides who will get the name.
But I'd be happy to hear what @Stuart Bowman  thinks of it. 

 Interesting, we needed you here for the conversation. I guess the naming conflict is still an issue if we want to reach people outside of our echo chamber. 

Do you mean handshakes with a DHCP server?

https://medium.com/@sajerestan/demystifying-the-dhcp-four-way-handshake-how-your-devices-connect-to-the-internet-a52f0c553a53

I also found some handshake stuff related to TCP:
https://www.geeksforgeeks.org/tcp-3-way-handshake-process/ 

 Sorry, I googled it myself and I didn't realize it's such difficult to find.
So here it goes: https://handshake.org
The idea originated from Aaron Swartz: http://www.aaronsw.com/weblog/squarezooko 

 nostr:nprofile1qqs07f7srjc72ma4skqrqmrm5a4mqdalyyw9k4eu2mjwwr9gtp644uqd4h7h8 do you remember what was on the corners of the unsolvable triangle? Perhaps we can only get all three corners under the assumption that users only care about content that is within their web of trust...  

 http://www.aaronsw.com/weblog/squarezooko 

 Thanks for sharing this. I need to re-read it more carefully, but my gut feeling says that proof of work can be used to distribute any scarce resource in a decentralized manner - namespace, address space, blockspace etc.. 

I've been thinking of using a combination of Bitcoin payment and barter (useful hashrate) for distributing IP addresses...