Yes, the quickest regionale takes 2h and 48 minutes.
Note that Regionales don't use the high speed tracks and the difference in speed isn't caused only by the number of intermediate stops: they run at 120 kms/h (if you are lucky) and any other train has the right of passage (not a big problem on the Naples-Rome line, but s**t happens).
Conductors can turn the AC off on Regionale trains, and, believe me, they'll do it if many elders complain about the AC being too strong.
Regionale tickets NOT purchased on the Internet are open, but they must be time-stamped before boarding; forget it and you'll be fined on the spot.
Then comes the quickest Intercity, taking 2h and 3minutes. Intercity trains have only reserved seats and discounted tickets can be purchased up to the day before the day of departure. They are meant for long travels and finding a place for your luggage will be easier. They are listed as IC on monitors and departure boards.
The quickest train run by Trenitalia on that route takes 1h and 8 minutes, it is the Frecciarossa1000 and it's also the most expensive train in Italy if you get tickets on the day.
Italotreno.it - the private competing company - runs only high speed trains between Rome and Naples and is often cheaper than Trenitalia.
Pick the stations closer to where you are staying. I bet this means Termini in Rome and Napoli Centrale in Naples, but if you were staying close to Tiburtina of course you would enter Roma Tiburtina as departure point.