Based on what you wrote above I do not see the problem of changing the page name would result in 404 errors on sub-level pages.
What you should look for
1- Check if you do not have active plugins like (The Event Calendar) or equivalents. Those plugins are already using, most of the time, those slug or rewrite rules.
2- You did not mentionned that you were using Custom Post Type, but if it would be the case, you can edit the rewrite rule to place your new slug (Codex : register_post_type)
function register_custom_post_type_example() {
$rewrite = array(
'slug' => 'calendar',
'with_front' => true,
'pages' => true,
'feeds' => true,
);
$args = array(
'label' => 'Your label'
'description' => 'Your description',
'supports' => array('page-attributes'),
'taxonomies' => array(),
'hierarchical' => false,
'public' => true,
'show_ui' => true,
'show_in_menu' => true,
'menu_position' => 20,
'menu_icon' => 'dashicons-networking',
'show_in_admin_bar' => true,
'show_in_nav_menus' => true,
'can_export' => true,
'has_archive' => true,
'rewrite' => $rewrite,
);
register_post_type( 'equipe', $args );
}
add_action( 'init', 'register_custom_post_type_example' );
In the code above, you can see that you can change the rewrite rule. But as I said, do not try to work with alot of plugin because it will results in pages conflicts.
Hope it can guide you to find the problem.