I couldn't find anything in the app to change the name, either.
All I can suggest is using the "Open In..." function to send it to another app for re-naming. For example, I was able to send a PDF from Adobe Reader to GoodReader, change the name there and then redo the "Open In..." function [from GoodReader] to re-open the newly named document in Adobe Reader.
IOW, it seems as if Adobe Reader is just a reader, not an editor (even just to rename files). Sorry.
Marilyn