Since I needed some time to find out how to change the user profile tabs title and page title, I'd like to share that information with you.
Drupal 7:
The below snippet changes the titles to static values and removes the dynamic page title callback:
If you need a dynamic title, for example with the user name included, you would instead replace the title callback with your custom callback. Keep in mind that this may also mean you have to remove the source file for the page title callback in that case.
Drupal 8
For Drupal 8 you might use https://www.drupal.org/project/user_current_paths as simple solution or have a look at its implementation.
Another alternative we created is https://www.drupal.org/project/better_user_accounts depending on your needs!
