Adding page Title in a custom coded page

function my_doc_title($title, $separator){
  if(is_author()) // <- replace this with your custom page; maybe is_page_template('myprofile.php') ?
   $title = get_the_author_meta('display_name', get_query_var('author')).$separator.get_bloginfo('name');
  return $title;
}
add_filter('wp_title', 'my_doc_title', 10, 2);

(functions.php)