generate random slug when adding taxonomy

You can use wp_insert_term_data:

add_filter( 'wp_insert_term_data', function ( $data, $taxonomy, $args ) {
    $data['slug'] = 'c8etv35n-c8etv35n-c8etv35n-c8etv35n'; // generate slug however you wish.
    return $data;
});

I found it in wp_insert_term function here.

But you should really implement ACL and not rely on random slugs to hide the content.