@mrwhosethesus
You do that yourself by embedding a link into the website you'd like to have displayed in green. See your Mastodon's settings.
@lunadev

@mrwhosethesus I hope you're not referring to the icon? :) Because anybody can put that behind their name.

But there are other ways of verifying, check the last section here:
https://docs.joinmastodon.org/user/profile/
And you do it yourself.

Luna's links are definitely verified by Luna. :)