Can not set custom title on some WordPress setups

This is most likely due to difference in your theme’s support. Some themes render the title by using the wp_title filter, some by using pre_get_document_title. If your theme has this line in its functions.php file:

add_theme_support('title-tag');

Then you need to use the pre_get_document_title filter, as follows:

add_filter('pre_get_document_title', 'my_title');
function my_title() {
    return 'Some title';
}

This is for the newer versions of WordPress. The old installations might be still using the legacy wp_title() function, which you already mentioned in your question.