Replace menu permalink/hyperlink with only menu name/slug

First of all –

I tryed to make this work to changing nav-menu-template.php

Never edit a core file! This is always a bad idea. At best, you will lose your changes when core updates.

To do this, you can use the nav_menu_link_attributes filter to modify the href attribute. This filter will be applied to each menu item individually.

In this example, we hook a function to the filter and str_replace the home_url with an empty string. So if our home URL is http://example.com, and the URL is http://example.com/something, the new value of href will be /something. We then return the modified attributes.

function wpdev_remove_home_url_from_menu_items( $atts, $item, $args ) {
    $atts['href'] = str_replace( home_url(), '', $atts['href'] );
    return $atts;
}
add_filter( 'nav_menu_link_attributes', 'wpdev_remove_home_url_from_menu_items', 10, 3 );

We only used the $atts argument in this case, but you’ll note that there are two other arguments- the menu item object and menu args, in case you need to do any checking of specific menu items or menus in order to decide how to modify the attributes.

You can also use this filter to add additional attributes, like data, rel, and target.