When referring to the modules installed on my Drupal site, how should I refer to them? Should I use the short name used from the module, or something else?
Use the name reported in the project page hosted on Drupal.org.
This will avoid ambiguity about the module being referred, especially when there are other modules that contains the same words in the project title (e.g. see the search result page for node reference).
Some modules are known by a short name (e.g. CCK, Ctools); if the short name is not used in the project page, possibly avoid using it.
If the module is not listed in this list, consider adding the link to the project page hosted on Drupal.org.