It’s called NIP-05 verification. Here’s a quick walkthrough and list of registrars you can get verified from: https://nostr.how/en/guides/get-verified 

 Unless you are verifying to your own domain verifying is pretty much useless. It's not actually verifying anything beyond a domain name.

Presenting this as a Twitter-like checkmark is bad UI. 

 all  @Coinos accounts come with a lightning address and can be used for NIP-05 nostr verification if you toggle that on in the settings page

https://m.primal.net/KTFu.png