We’ve kept a note of this feature and we’ll prioritize it if we have more users asking for it.
AyushGeorge Hooper commented
I have the same problem, and have seen it on other forums by others. When viewing a series of documents you don't create which happens very often in the work environment, or even at home when viewing a number of bank statements, for example, the document titles are often the same. The tabs are useless to identify the contents, so you end up clicking back and forth between tabs trying to remember which is which. Computers should do the work for us...
I did see a solution (below) for Adobe X Pro, could this not be applied to Acrobat?
Create an Acrobat X Action (Acrobat X Pro required).
Use "Set Open Options" from "Document Processing".
For Display Document Title select "No".
The result will be the PDF file name being displayed.