I am wondering if there is a way that I can change the page titles so that users can see a nice title but that at the same time, the internal title of that same page be different?
You can use a module that allows you to change it each time or use a different pattern than default Drupal:
This module allows you to control a lot more than just the Page title.
You can modify the title via a preprocess function in .theme file. For example a theme_preprocess_page function