Yes, if you have Acrobat Pro.
You can then create a batch process that adds the file's name as a watermark
to each page.
May i ask you how to create a batch process plz?
Creating a Batch Sequence using Acrobat Pro -
--| Select, from the menu bar, Advanced > Document Processing > Batch Processing
The Batch Sequence dialog presents itself.
--| Click the 'New Sequence' button.
The Name Sequence dialog presents itself.
--| Enter a name for the new sequence (e.g., "Add Watermark").
The Edit Batch Sequence - Add Watermark dialog presents itself.
--| Click the 'Select Commands' button.
The Edit Batch Sequence dialog presents itself.
The left side column lists commands; under the 'Document' folder -
--| Select 'Add Watermark' and then click the 'Add >>' button.
--| Click the 'Edit' button.
The Add Watermark dialog presents itself.
Configure as desired. Note the links "Page Range Options" (upper right) and "Appearance Options" (left side, just below center).
You may want to use these options as part of the Watermark's configuration.
When configuration within the Add Watermark dialog is complete, click OK.
OK out of the Edit Sequence dialog.
Back in the Edit Batch Sequence - Add Watermark dialog continue with configuration options as desired.
Note: There is a square adjacent to the "Add Watermark" command that was selected.
For unattended operation, leave this box NOT ticked.
Clicking the 'Output Options' button provides access to a dialog from which you can choose to utilize PDF Optimizer.
The 'Settings' button provides access to PDF Optimizer's configuration dialog.
With all desired configuration complete, OK out of the Edit Batch Sequence - Add Watermark dialog.
Click the 'Run Sequence' button to run a selected Batch Sequence.
The configuration selection made for "2. Run commands on:" (in the Edit Batch Sequence - <name of sequence>) determines what you will observe next.
So - Some other information associated with PDF document's file name -
(try67) posts at AUC:
"Print File Name with pdf Document" thread from this Forum (an older thread, but informative).