Get the name of menu item with wp_nav_menu

The object_id holds the ID of whatever object the menu item refers to, this will be a post, post etc. The get_queried_object_id() will give you the ID of the current page. 

$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;

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