Identify and display the fact that user is admin next to username in comment section

From inside a comment Loop…

$author_data = get_user_by('login',$comment->comment_author);
if (!empty($author_data)) {              
  var_dump($author_data->roles);
}

$author_data->roles is an array so you will need to work out what you want to do with that. That is, print them all? Print the highest ranking role?

if (array_intersect(array('administrator','moderator'),$author_data->roles)) {
  echo 'admin';
} elseif (array_intersect(array('something','else'),$author_data->roles)) {
  echo 'something else';
}