How to change the blog title with add_filter? details below

With the filter single_post_title, you can change the page/post title that is set in the <head><title>Page title</title></head>.

If you want to change the title that you see in the page header. ( Which i think you want to do).

Use this filter:

add_filter('the_title', 'modify_all_titles', 10, 2);

function modify_all_titles($title, $id) {
  return 'SOME TEXT BEFORE TITLE | '.$title;
}

Place this code in the functions.php (use a child theme).

Regards, Bjorn