What is a verified user?
It's a user that has been exclusively trusted on a certain router. This user cannot be troll-tagged, and appears on top of the client list.
How to become a verified user?
You'll need to add some stuff to your demonsaw.toml file (see links below). The produced hash will need to be specified in the .toml file of the router you connect to. The next time you connect to this router, you will generate a hash based on what you have in your .toml, and send it to the router. The router will check if this hash equals the hash specified in its .toml, and announce your verification to all connected clients.
To learn how to implement the verified version on your own router please check the router tutorial and client tutorial.
Router tutorial: Router Setup
Client tutorial: Client Setup