Change the site name programmatically for a specific page
I think you mean page.tpl.php (not system.tpl.html, which isn't a standard Drupal file).

That said, you need to put your code in a hook_preprocess_page() function inside template.php, and actually alter the template variables that are passed in. At the moment you're just creating a variable called $site_name in the local scope, and Drupal has no way to pick that up.

Try this:

function MYTHEME_preprocess_page(&amp;$vars) {
  $path = drupal_get_path_alias();
  if ($path == 'about_us') {
    $vars['site_name'] = 'New title';
  }
}


Have a look at Setting up variables for use in a template for a bit more info.