Title showing 'Home' on Tabs
The page title is by default the title defined in hook_menu for the menu item. If you want to alter the title, you should use drupal_set_title.

Note: Drupal set title can't be used to late in the theming process (like template_preprocess_page), as the value for the title has already been populated at that point. Using it in the menu callback should work just fine.