Can Hazel save and name email attachments?

I get 40 separate emails with attachments that I need to save to a folder, but they all have the same name. The only way I can tell the attachments apart is by looking at the subject of each email, then manually naming the files as I save them.

Is this something Hazel can do?

It might. I forget it the subject is in the metadata but if not, you can try matching on the file contents. If you haven't already, download and install it to run the trial.