How to print filename as header/footer for lots of PDF?

I need to print a lot of PDF files that came from suppliers in order to file paper copies. It would help immensely if I can print (whether from Preview, Adobe or even something I must buy) in such a manner that the filename always appears on the printed copy. We're talking about a lever arch file, so going through them individually to create a new version of the PDF with the actual filename appearing in the PDF image is not really an option.

I'm a little surprised that there isn't such an option in Preview (or Adobe for that matter).

Would be much appreciated, thanks