Change Parent Name with wp_list_pages?

method1.php

<?php
/**
 * Method 1: Use the the_title() filter to modify the first link name in wp_list_pages(). 
 * 
 * @see http://wordpress.stackexchange.com/questions/156742/change-parent-name-with-wp-list-pages
 */
 
// -----------------------------------------
// Place this wpse_title() function definition into 
// the functions.php file in the current theme directory.
//
function wpse_title( $title )
{
    remove_filter( current_filter(), __FUNCTION__ );
    return __( 'Overview' );
}
// -----------------------------------------

    if ( is_page() ) {
    $parent = get_post($post->post_parent);
    $parent_title = get_the_title($parent);
    $grandparent = $parent->post_parent;
    $grandparent_title = get_the_title($grandparent);
    $current_page_parent = ( $post->post_parent ? $post->post_parent : $post->ID );

    // is the homepage the granparent? = third level page
    if ($grandparent == is_page('0')) {

        // Begin Mod:
        add_filter( 'the_title', 'wpse_title' ); 
        $children = wp_list_pages("title_li=&include=".$post->post_parent."&echo=0"); // list the parent page
        // End Mod.
        
        $children .= wp_list_pages("title_li=&child_of=".$post->post_parent."&echo=0"); // append the list of children pages to the same $children variable
        if ($children) {
            ?>
            <ul class="submenu">
              <?php echo $children; /*print list of pages*/ ?>
            </ul>
        <?php
        }

    // is the homepage the parent? = second level page
    } elseif ($post->post_parent ==is_page('0')) {
        $children = wp_list_pages('title_li=&child_of='.$post->ID.'&echo=0');
        if ($children) {
            ?>
            <ul><li class="current_page_item"><a href="<?php echo get_permalink( $parentid ) ?>">Overview</a></li><?php echo $children; ?></ul>
        <?php
        } else {// your else stuff
        } } }
?>

method2.php

<?php
/**
 * Method 2: Construct a direct link above wp_list_pages(). 
 * 
 * @see http://wordpress.stackexchange.com/questions/156742/change-parent-name-with-wp-list-pages
 */

 if ( is_page() ) {
    $parent = get_post($post->post_parent);
    $parent_title = get_the_title($parent);
    $grandparent = $parent->post_parent;
    $grandparent_title = get_the_title($grandparent);
    $current_page_parent = ( $post->post_parent ? $post->post_parent : $post->ID );

    // is the homepage the granparent? = third level page
    if ($grandparent == is_page('0')) {
        $children = wp_list_pages("title_li=&child_of=".$post->post_parent."&echo=0"); // append the list of children pages to the same $children variable
        if ($children) {
            ?>
            <ul class="submenu">
              <li>
                  <a href="<?php echo get_permalink( $post->post_parent ); ?>">Overview</a>
              </li>
              <?php echo $children; /*print list of pages*/ ?>
            </ul>
        <?php
        }

    // is the homepage the parent? = second level page
    } elseif ($post->post_parent ==is_page('0')) {
        $children = wp_list_pages('title_li=&child_of='.$post->ID.'&echo=0');
        if ($children) {
            ?>
            <ul><li class="current_page_item"><a href="<?php echo get_permalink( $parentid ) ?>">Overview</a></li><?php echo $children; ?></ul>
        <?php
        } else {// your else stuff
        } } }