I decided to update some of my older downloads from GOG and noticed that the newer version of Dragonfall Director's Cut no longer had Director's cut in the file name. Is it just a matter of not including the name or are the wrong files linked to the download section? Obviously I am talking about the offline installers.

The current filename is:
setup_shadowrun_dragonfall_2.0.9_(9992)

I have only purchased the Director's Cut, and is the filename of the game I downloaded (back in April 2017).

Same here, just that the previous version I have is titled
setup_shadowrun_dragonfall_directors_cut_2.1.0.7

From the previous time I downloaded it a couple of years ago.

I was wondering why the change of name.

The week before I downloaded the above version, the theretofore most-recent file was named:
setup_shadowrun_dragonfall_directors_cut_2.1.0.8
but I cannot tell you, absent any official knowledge, why the name was changed.
Maybe someone from CD-Projekt might tell you.
*casts conjure Admin* … [this may take a moment …]