File Name Stamper

It's certainly possible to do it in the current version of Acrobat Pro. The Action you found might be outdated, but there are others out there that aren't.

If you open any document, you will see the full name of the app at the file name bar at the top. If it doesn't for some reason show there, just go to the Acrobat Help menu and show About Acrobat...  you will see the word "Pro" there.

As for your action, I can't speak to how well it works (if at all) in the current versions, but you can certainly install it and try.

I see in this product instructions that this Action is only compatible with Adobe Acrobat X Pro and Adobe Acrobat X Pro Suite.  Sounds like I am not going to find any ability to use this Action unless I purchase another version of Adobe.