Set different page and window titles
In Drupal 7, the template file that sets the title shown in the browser page is html.tpl.php, while the template that sets the page title is page.tpl.php.  

Both the templates don't receive a variable containing the user object to which the page is referring, as those templates are used for every page. If you want to change the titles only for user pages, then you need to get the user object using menu_get_object('user'). The function returns FALSE if the currently shown page is not a user profile page; that is what happens when the viewed page is, e.g., example.com/node/1.