PSA: The "verified" symbol you see on Twitter etc means absolutely nothing on Mastodon or the Fediverse. On here, symbols like are just custom emoji that anyone can use and put after their name. Don't be fooled! 😁
There are ways to verify your identity on here, but the symbol is not one of them.
The easiest way to verify your identity is if you have a website that people already know is yours. You can paste a special code into your website which will verify your address and it will turn green on your Mastodon profile (see here for instructions: https://mstdn.social/@feditips/106274105538953001).
Alternatively, you can set up a server as a subdomain of your known website address. For example, the European union set up their own Mastodon server at https://social.network.europa.eu, and we know it really is the EU because the server address is part of the EU's well-known europa.eu domain.
p.s. If you want to see an example of a verified link on Mastodon, try looking at the profile of @libreoffice
Unfortunately the verified links aren't visible on the official apps yet, so you would need to do this via the website or a third party app.
I've included a screenshot so you can see what I mean.
My server, my rule, invite only, but part of the Fediverse. Do join Mastodon on any server, and follow...