add_menu_page() with different name for first submenu item

You can make the ‘slug’ for the submenu page equal that of the top level page, and they’ll point to the same place:

add_action('admin_menu', 'my_menu_pages');
function my_menu_pages(){
    add_menu_page('My Page Title', 'My Menu Title', 'manage_options', 'my-menu', 'my_menu_output' );
    add_submenu_page('my-menu', 'Submenu Page Title', 'Whatever You Want', 'manage_options', 'my-menu' );
    add_submenu_page('my-menu', 'Submenu Page Title2', 'Whatever You Want2', 'manage_options', 'my-menu2' );
}

E.g.