Returning a car rental to Rome Fiumicino and then taking the fast train to Naples

Why not return the car at Termini Centrale and not have to travel to a train station to get the train for Naples?

If you must return the car at FCO, this may be an alternative -- https://www.fiumicinoexpress.com/bus-rome-fiumicino-airport-to-naples/?lang=en

I’ve read says to pre purchase the train tickets,

if you have read good sources, they say to purchase asap to save money. Do you need / want to save money? If not, why running the risk of wasting a train ticket?

I assume you cannot exchange the time of the train

This question makes me think that the things you have read did not provide the relevant info about train tickets. Discounted tickets can't be changed and/or refunded, if you are late and miss the booked train you must buy a new ticket. If you arrive earlier than expected, you have to wait for the booked train.

On the other hand, when you pay the top, Walk-up fare the tickets can be freely exchanged before and after the departure of the booked train. But... why would you buy in advance a ticket paying the walk-up fare? Nevertheless, both Trenitalia.com and Italotreno.it show the walk-up fares together with the discounted ones, so you know how much you'll pay getting tickets on the day of travel.

is it easy to get tickets at the station?

Both Trenitalia's and Italotreno's ticket machines are multilingual and use the same user interface of the relevant web pages. If you find those sites easy to use at home, the ticket machines at Termini won't be more difficult.

Since there is free wi-fi at Termini station, you could install the 2 apps at home, get used to them on your couch and buy online by the tracks.

If anything else fails, head to the closest counter and hand them a note saying "Napoli Centrale, solo andata, Alta Velocità". They will put you on a train departing within 15 minutes or more.

have a private car pick us up

Ask the driver if he/she'd rather pick you up at Napoli Afragola station. Afragola is way less crowded than Centrale, but let the driver decide.

I agree with the above message, what's the point of droppin' the car at the airport when you are headed to the train station?

I am with Joe. Return the car to Termini and take the train from there. The only reason to buy tickets in advance is to take advantage of available discounts. All discount tickets cannot be changed so if your schedule is uncertain, then you buy the tickets when you get to the station. You can buy full fare tickets at anytime and exchange them within 90 minutes if you miss the train. (The 90 minutes may recently been changed to 60 -- that you need to double check.) The train from the airport goes to Termini.

Where are you driving from?
I wonder if it wouldn't be easier to drive to Naples airport, drop the car there, and get picked up there. The 2.5 hour drive between Rome and Naples is boring, but depending on where you are coming from, you might actually save time and hassle.

We are renting the car in Rome upon arrival, driving to Pienza and want to be able to see the surrounding areas there, and then had planned to return the car to the same rental (Avis) center and then take the train from there Prefer not to drive to Naples

There is an Avis rental at Termini. You could rent from there as it is fairly easy to get out of town from Termini. You have a number of options. Even if you rent at the airport, there should be no drop fee if you return to Termini.

I did not know that! I will definitely look into that! Thank you everyone!

Even if you rent at the airport, there should be no drop fee if you
return to Termini.

I have spent the past few months checking car rental rates and options using every pick up/drop off, agency imaginable and ALL are now charging a drop off fee.

last time we rented in Italy that was not the case.
I'd be surprised if OP finds a quote with no drop off fee and if you do could you let me know where? :)

getting train tix is easy at the station or download both Trenitalia and Italotreno apps and use those as Dario suggested- super easy.

OP- another option for travel to Positano is take the fast train from Termini to Salerno- then direct ferry to Positano- (as long as your trip is when ferries are running- April- Oct)

Taking the train to Salerno and then the ferry to Positano sounds wonderful, but I've read it all depends on the sea that day....?

True
Ferry stops in Amalfi first and that dock not as affected by weather as much as Positano

You can also take bus from Salerno to Positano
Or ferry from Salerno to Amalfi then bus to Positano

Some folks like to rent or return from the Avis office near the Tiburtina rail station since you don’t hav3e to navigate as many local streets. It is very close to both the SR5 and the A24. I returned a car once at Termini and driving to the station was not too pleasant - sort of like a rat in a maze. Neither was finding the garage where the car had to be returned.
Unless you must rent from Avis, consider checking rental costs at AutoEurope. They are often less expensive. I went to the Avis website, got a quote for pickup at FCO and return at Tiburtina (Via Teodorico). A Fiat 500X for 1 week was $629.23 including a one way fee of $120.01. At AutoEurope, a Fiat 500L was $343.89 including a one way fee of $15.24.

We found it cheaper and easier to return the rental car to Naples airport which is near the Autostrada above the city center. We felt we won twice with easier travel and less expensive too! Drive on autostrada is easy!

From Pienza, driving all the way to Naples airport only takes 90 minutes longer than driving to Termini, since you bypass Rome altogether.
So if you are able to find a good rate for a Rome-Naples car rental, you will save time and a bit of hassle (getting from car rental to train with luggage, then again to your pickup point at the station). Naples airport is seconds away from the highway, so you do not have to deal with the craziness of Naples driving.

Otherwise, the suggestion to ditch the private shuttle altogether and take the train to Salerno instead, isn't bad at all!

From Pienza to Positano these are the options:
MINIMUM CAR USE OPTION:
Return the car at Avis Autonoleggio - Chiusi
+39 0578 226878
https://goo.gl/maps/5iNr9bAsPBW23QJt9
Take the train from Chiusi to Salerno or Naples (one train change in Rome).
From Naples or Salerno you can use a private car, but from Salerno you could have also the ferry option to Positano.

MAXIMUM CAR USE OPTION
Drive rental car to either Salerno or Sorrento. No need to go to Naples at all. The drive is easy (newrly all freeway, albeit long (5-6 hours). Both towns have Avis agencies near the train stations. From Salerno to Positano you can take the ferry. From both you can take a taxi, private car limo, or even a bus.

If It were my trip, actually I would drive all the way to Positano myself, drop off the bags at the hotel, then either park the car in a Positano parking lot, or, if you don’t need/want the car anymore, drive to nearby Sorrento to return the car. Then, from Sorrento, since you are already unencumbered by the luggage, I would take the bus back to Positano.

The option you’ve chosen, to return the car in Rome (which is half way between Pienza and Positano), then the train, to me is the most inconvenient and convoluted.