(not verified) appears on registered users

got the same problem don't know what happen until I saw this post. So I look into the code and noticed that you have to enable profile module, but I saw you have already solve this issue :)

This is actually a bug caused by the following code:

  if ($object->uid && $object->name && module_exists('profile')) {
    
    profile_load_profile($object);
    if (!empty($object->profile_real_name)) {
      $object->name = $object->profile_real_name;
    }
    
    // Shorten the name when it is too long or it will break many tables.
    if (drupal_strlen($object->name) > 20) {
      $name = drupal_substr($object->name, 0, 15) .'...';
    }
    else {
      $name = $object->name;
    }

    if (user_access('access user profiles')) {
      $output = l($name, 'user/'. $object->uid, array('attributes' => array('title' => t('View user profile.'))));
    }
    else {
      $output = check_plain($name);
    }
  }
  else if ($object->name) {
      // Sometimes modules display content composed by people who are
    // not registered members of the site (e.g. mailing list or news
    // aggregator modules). This clause enables modules to display
    // the true author of the content.
    if (!empty($object->homepage)) {
      $output = l($object->name, $object->homepage, array('attributes' => array('rel' => 'nofollow')));
    }
    else {
      $output = check_plain($object->name);
    }

    $output .= ' ('. t('not verified') .')';
  }

If profile.module is not installed, then the code executes the else if ($object->name) { branch, which will print the "not verified" close to the user name.
That is indeed wrong, as that string should be printed only if the user object has a property name, but not a valid user ID. I am not sure in which cases this could happen (maybe when a user has been delete from a Drupal site, but his posts are still present in the site), nor I am sure that could be the correct thing to do (if a user was authenticated on a Drupal site, why should he be not verified?).

Committed a fix that moved the profile module check to just around the object->name def. A new release will be out soon.

As a side note to the question, "(if a user was authenticated on a Drupal site, why should he be not verified?)" - if you are using an external authentication module like LDAP Integration http://drupal.org/project/ldap_integration
it's possible for user records to be created with no email address, (which seems to be the definition of "not verified" in the core?).

I added the Real Names module http://drupal.org/project/realname which worked as a workaround for some reason but I like this answer.

Speaking of http://drupal.org/project/realname and this issue, FYI: realname can actually cause this 'not verified' issue ('not verifed' behind verified usernames, displayed to users not logged in) if configured without proper understanding. At admin/user/realname the "Show "Not verified" for anonymous users" checkbox at the bottom may cause this issue if one doesn't realize how this option works. Also, when using realname, don't forget to set permissions. ;)