AFAIK it's impossible. Current Bitcoin P2P Networking[1] doesn't seem to have any call to request arbitrary data (which could be stored to request proof of identity). And while i don't know what you're trying to achieve, have you checked bitnodes website[2]? They collect and combine data they could get from other Bitcoin nodes.

[1] https://developer.bitcoin.org/reference/p2p_networking.html#version
[2] https://bitnodes.io/