Out of the box, Drupal puts (not verified) next to user information for anonymous users. For example, when an anonymous user submits a comment (not verified) appears next to their name. This is handy for community sites where you need to distinguish between who is a member and who isn't. For sites, like a single user blog, the (not verified) doesn't fit. So, one of the first things I do when a fresh new major release of Drupal comes along is learn how to remove the (not verified).
In past versions of Drupal removing the (not verified) happened thought the theme system and theme_username. When I took a look inside theme_username in Drupal 7 I found it had been entirely rewritten and there was no sign of (not verified). Luckily, I didn't need to trace through the code to figure out where to remove it. This is such a common change there is now a setting for it.
To get to the setting go to Appearance in the navigation and then click on settings for the theme you want to remove it from.
Scroll down to the Toggle Display section and uncheck User verification status in comments. Click on Save configuration at the bottom to save the changes and you're done.
If you have multiple themes and want to disable the (not verified) in all of them you can do that in the Global settings. The setting is in the same place as an individual theme on the Global settings page.