you should have a look at FileJuggler: http://www.filejuggler.com
FileJuggler is a little, but powerful tool that offers file automatization based on information from file name, file properties or from file contents (for OCRed PDF files). You can define one or multiple folders to be monitored by FileJuggler as well as rules and actions to be applied. Renaming your sample file by the date printed in the document should be a breeze with FileJuggler. Just tell the tool which folder to monitor, define a move-action (to move processed files from the monitored folder to some other place) and a rename-action with the filename defined as [file contents: date]_rest of the filename[file extension]
. In the end you will have your files moved to the other folder and have them renamed like 2016-07-06_rest of the filename.pdf
(or anything else you define).
If you download the (quite stable) Beta from the Website you have much more sophisticated variables than in the current release. A 30-day-trial is free. The full Version is 25$ - worth every penny.