Wordpress: Set display name with 'first name'

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/* Sets the user's display name (always) to first name last name, when it's available **************************************
** http://stackoverflow.com/questions/9326315/wordpress-change-default-display-name-publicy-as-for-all-existing-users *** */
/* !아이디 대신 이름으로 나타내기 ********************************************************************************************* */
/* Sets the user's display name (always) to first name last name, when it's avail. */
add_action ('admin_head','make_display_name_f_name_last_name');
function make_display_name_f_name_last_name(){
    $users = get_users(array('fields'=>'all'));
    foreach($users as $user){   
        $user = get_userdata($user->ID);
        $display_name = $user->first_name;
        if($display_name!=' ') wp_update_user( array ('ID' => $user->ID, 'display_name' => $display_name) );
            else wp_update_user( array ('ID' => $user->ID, 'display_name' => $user->display_login) );
        if($user->display_name == '') 
            wp_update_user( array ('ID' => $user->ID, 'display_name' => $user->display_login) );
    }   
}

tank you

It will only show the first name even though I have a last name. Is there anyway to show it as first and last name?

@angemman I did make some modification on code to show first and last name:

// Sets the user's display name (always) to first name last name, when it's available

add_action ('admin_head','make_display_name_f_name_last_name');
function make_display_name_f_name_last_name(){
$users = get_users(array('fields'=>'all'));
foreach($users as $user){
$user = get_userdata($user->ID);

    // get first and last name
$first_name = $user->first_name;
$last_name = $user->last_name;

    // trim to 'full name' string
$display_name = trim( $first_name . ' ' . $last_name );

    if($display_name!=' ') wp_update_user( array ('ID' => $user->ID, 'display_name' => $display_name) );
        else wp_update_user( array ('ID' => $user->ID, 'display_name' => $user->display_login) );
    if($user->display_name == '') 
        wp_update_user( array ('ID' => $user->ID, 'display_name' => $user->display_login) );
}   

}