You could use a script and set a variable $Filename in that script.
Save the PDF with $Filename as output file.
Than set a field with as calculated result $Filename.
I added a sample file.
The script name is Add product PDF, go to the product menu to test it. (you can change the save path) under the settings button or in the script.
Hope it helps.
Sample add PDF.fmp12.zip 2.1 MB