Non-stop train from Rome to Assisi?

No but there are about three direct trains but I don’t know if they are per day taking 2h 15m.

There are no non stop trains to Assisi from Rome, and I would be shocked if there were.
There are direct trains to Assisi, but they make stops along the way.

Assuming you mean "direct", on Trenitalia's search results page the number of changes is listed in the 3rd column, headed Duration.

If you click the small grey " i " near the train codes, you'll see the intermediate stops before your arrival station.

In summer 2019 we took a train from Rome (Termini Station) to Assisi. It did make stops along the way, but we never had to change trains or make transfers. As I remember some trains were marked ‘regional’ or something like that and those trains took much longer and made a lot more stops. You’ll see the stops and duration when you choose the ticket. We chose a train that made fewer stops and probably took 2-2.5 hours or so, if I’m remembering correctly. We got an early start and made it a day trip to Assisi. Easy to do.

I believe all the trains stopping at Assisi are regionals. You might find a routing that starts with a faster train and then requires a change to a regional somewhere along the way; I see one such departure with a change at Foligno. It's important to look carefully at connections like that, because including a fast train in the routing drives up the ticket cost, but any time advantage can be lost due to the layover when you change trains.

Thanks for the great advice!