Is there any id on the handles, wall plate anything that might id it as moen, delta, etc? I would give that stem a good cleaning and see if anything shows up especially at the end opposite the white end. A wire brush or similar should get rid of most of that crud. I'm not sure what a 2 means but there are some pretty wise helpers on this site so be patient. You might also go by your local hardware store with the part and see if they can id it for you. It looks pretty standard and that's maybe why there's only a #2 stamped on it. Also, all the major manufacturers have a "how to id your cartridge" style app on their web sites and that can help. Wish it was simpler.
HomeDepot sometimes has a book with photos of different cartridges/valve stems. If it is safe for you to go to your nearest one, you can take it to the store & have them compare to see if anything matches it. I'd call ahead of time to make sure they have the book though. They usually have it in the section where they sell replacement cartridges & they can sometimes order them if they don't have them in stock.