Add Real Names (u.signature) to Admin/User/User/List?

As admins we want to see the user's "Real Name" and not just the UserName as listed on the

.../admin/user/user/list? Page.

The only way I see to make an "add a column" change to this page is to edit

.../modules/user/user.admin.inc

I have "almost" got it... The real name is stored in the user.signature column
and I want to add this column to the .../list page above as the second column.
So I added, starting at line 129, one new line with u.signature in it and
the addition of u.signature to the $sql line:

function user_admin_account() {                                                                                            
  $filter = user_build_filter_query();                                                                                     
  $header = array(                                                                                                         
    array(),                                                                                                               
    array('data' => t('Username'), 'field' => 'u.name'),
    array('data' => t('Name'), 'field' => 'u.signature'),   
    array('data' => t('Status'), 'field' => 'u.status'), t('Roles'),                                                       
    array('data' => t('Member for'), 'field' => 'u.created', 'sort' => 'desc'),                                            
    array('data' => t('Last access'), 'field' => 'u.access'),                                                              
    t('Operations')                                                                                                        
  );                                                                                                                       
  $sql = 'SELECT DISTINCT u.uid, u.name, <strong>u.signature,</strong> u.status, u.created, u.access FROM {users}...

I also edited the code starting at line 911 by adding the Name(Sig) header and u.signature line
and added the next to last drupal_render line.

function theme_user_admin_account($form) {                                                                                 
  // Overview table:                                                                                                       
  $header = array(                                                                                                         
    theme('table_select_header_cell'),                                                                                     
    array('data' => t('Username'), 'field' => 'u.name'),                                                                   
    array('data' => t('Name(Sig)'), 'field' => 'u.signature'),
    array('data' => t('Status'), 'field' => 'u.status'),                                                                   
    t('Roles'),                                                                                                            
    array('data' => t('Member for'), 'field' => 'u.created', 'sort' => 'desc'),                                            
    array('data' => t('Last access'), 'field' => 'u.access'),                                                              
    t('Operations')                                                                                                        
  );                                                                                                                       
                                                                                                                           
  $output = drupal_render($form['options']);                                                                               
  if (isset($form['name']) && is_array($form['name'])) {                                                                   
    foreach (element_children($form['name']) as $key) {                                                                    
      $rows[] = array(                                                                                                     
        drupal_render($form['accounts'][$key]),                                                                            
        drupal_render($form['name'][$key]),                                              
        drupal_render($form['signature'][$key])
        drupal_render($form['status'][$key]),           

I *Almost* have it... the page renders with the proper header "Name(sig)" and it is clickable
for sort, But No signature column values show. No "Real Names show.

Can anyone direct me to what I am missing? There must be another place where I need
to make the user.signature column part of the search results.

AND as a bonus, there is probably a better way to do this without digging into the core
modules folder. Suggestions?

Much Appreciated.

-Bob O