How to customize the HINT in the Menu

That “Hint” is better know as the link’s title attribute. On Page links, it normally defaults to the page title. On category links, it can used to display the category’s description.

https://codex.www.ads-software.com/Template_Tags/wp_list_categories

Yes – but how to change the default value for the pages? Any trick? Thanks.

You can’t. It’s built into the core for wp_list_pages.

Ok -ùi see
title_li’ => __(‘Pages’),

May be we can change (‘Pages’) for some php function that would get its value from conditions – something like (if ‘page’ is ‘Home’ then title is ‘some words’) etc. That is an idea – ?

title_li' => __('Pages'), means “give this list the heading title of Pages”. It has nothing to do with the link title attribute. Your only coding option would be to abandon wp_list_pages in favour of a “roll your own” page listing using something like get_pages().

Ok- thanks. A simple need get complicated.