"notice: Undefined property: stdClass::$name in theme_username() (line 1668 of includes\theme.inc)"

theme('username', drupal_anonymous_user())

produces the notice above because the name member is not set.

I propose adding the highlighted line below:

function drupal_anonymous_user($session = '') {
  $user = new stdClass();
  $user->uid = 0;
  $user->name = '';           // Can we add this line?
  $user->hostname = ip_address();
  $user->roles = array();
  $user->roles[DRUPAL_ANONYMOUS_RID] = 'anonymous user';
  $user->session = $session;
  $user->cache = 0;
  return $user;
}