How I can change the way the submitted forms PDF's are named?

We would like to customize the file naming process as we get the submitted forms, vs just being named with 17 random numbers.  Can this be done?  

Unfortunately, renaming the PDF in the notification email is not possible at this time. The string of number in the file name is the submission ID.

You may consider integrating the form to Google Drive and use custom folder name:

https://www.jotform.com/help/192-How-to-Integrate-a-Form-with-Google-Drive,

You will have to get the PDF from your Google Drive account.

Or, Dropbox:

https://www.jotform.com/help/77-Upload-to-Dropbox-with-JotForm