Display user name with flags
I don't know the particular flag api to get the usernames of flagged node.
But it can be possible using custom implementation. Here is code 

function get_usernames_flagged_node($entity_id, $flag_name) { //Supply node_id and flag_name
  $get_all_nodes_of_flagged = flag_get_flag_flagging_data($flag_name);
  $flagged_content_detail = array();
  $username = array();
  foreach($get_all_nodes_of_flagged as $get_all_nodes_of_flags) {
    $flagged_content_detail[] = $get_all_nodes_of_flags;
  }
  foreach($flagged_content_detail as $flag_content) {
    if($entity_id == $flag_content-&gt;entity_id) {
     $user=user_load($flag_content-&gt;uid);
     $username[]=$user-&gt;name;
    }
  }
  return $username;
}


It can be also possible using views and flag modules. For your reference see this page