How to get current page menu item name instead of full menu item list

I would like to build a menu structure where you can only see the menu item of the current page like on this web site http://www.bigspaceship.com/services/

I search around and I have the following function so far

<?php
$menu_items = wp_get_nav_menu_items( 'main-menu' );
foreach( $menu_items as $item ) {
  print_r( $item ) ; // see what you can work with
  // carry on
}

How can I actually print only the menu item name for the current page?
I want to still control the menu item from the dashboard meaning I want to be able to change the name of each menu within the admin and have them dynamically update.

Thanks for any help.

1. Within each menu item, object_id holds the ID of whatever object
   the menu item refers to. This will be a post / page / CPT / term ID. If it’s a custom link, the ID refers to itself. (If you want to know what type of object it is, object contains that.)

2. get_queried_object_id() will give you the ID of the current page.

3. We can use the API function
   wp_filter_object_list()
   to filter out any menu items where the object_id doesn’t match the
   queried object.

4. We’ll then be left with an array containing a single element, so we
   use php’s current so that $this_item now contains just the
   matching menu item object.

5. and finally, title holds the name we’ve given the menu item.

$menu_items = wp_get_nav_menu_items( 'main-menu' );
$this_item = current( wp_filter_object_list( $menu_items, array( 'object_id' => get_queried_object_id() ) ) );
echo $this_item->title;

Note- I didn’t test this, so hopefully it works!