I am traveling from Orvieto to Naples. There is a 15 minute connection in Rome. Is that even possible to make?
yes
As long as your train is not delayed, sure it is. And if you do miss it, there are departures for Naples nearly every hour, your ticket would still be good on the next one (but not your reservation if you have one).
Best,
You probably can make it if you're a Rick Steves type traveler (eg 1 carry-on bag per person). If you have a whole array of bags to be carried or pulled then it becomes dicier.
As mentioned above, 15 minutes is fine if your train is on time. You are most likely on a Regionale train from Orvieto to Rome and these trains are sometimes held in small stations as the high-speed non-stops whiz by. Still, you should be fine. PACK LIGHT. The 3 stairs onto and off of the train carriage are a bit steep. You will struggle with a lot of luggage.