Skyphe.org

By default, WordPress will notify only the actual post author if there are new comments on their post. But what if you want to notify additional people about every comment posted on the website? Like site editors, for example?

This is just a quick filter you can use in this case:

function filter_comment_notification_headers( $message_headers )
{
    $notify_other_people = array(
        '"John Smith" <john.smith@email.address>',
        '"Jane Smith" <jane.smith@email.address>'
    );

    $message_headers .= "\n" .
        'CC: ' . implode(', ', $notify_other_people );

    return $message_headers;
}
add_filter('comment_notification_headers', 'filter_comment_notification_headers');