Using a DLSR I can think of a few ways, all of them would involve some kind of scripting or post-process though. Essentially you need to know what product was in front of the camera and when. Depending on how often you'll need to do it will determine what level of automation you can/should bring to bear.

The most low-tech solution would be to take a leaf out of the videographers book and shoot a whiteboard or chalkboard with the details of each product before you shoot it. Then when you go through in post using bridge or similar the title frames will be obvious for manual renaming or tagging.

Alternatively you could log when each product is shot using a tablet/laptop like matching up a GPS log. As long as you sync the times up it would be relatively simple for someone with the appropriate skills to write an app/script to do that for you.

Or there is the eye-fi option mentioned by AJ. Again, that can be automated fairly easily to automatically add a tag/rename files as they appear.