How to hide home title on pages and posts?

If I follow what you’re explaining correctly, try adding a document title filter to the functions.php theme file. (NB: setting to only change post and pages. Search, Archive, etc, will keep original title. You can always modify accordingly.)

*** EDIT: added a filter for older themes that uses wp_title.

add_filter('wp_title', set_custom_page_title, 99999); //NB:backward compatibility with wp_title() theme function
add_filter('pre_get_document_title', set_custom_page_title, 99999);
function set_custom_page_title($orig_title) { 
    if(is_page() || is_single()){
        return get_the_title();
    }
    return $orig_title;
}