Changing trains in Naples

They should be if you are on your toes and move quickly. Often times it is no more than walking 20 feet to the outside of the platform, or down the stairs, up the stairs to the next platform. In Naples, Garibaldi is down the stairs and 50 yards (?) to the platform. Generally signage is pretty good.

It really does not matter. I am assuming the transfer is to the Circumvesuviana train which runs often. It is like a commuter train. It is one floor below the main train station and you buy your tickets there. Ten minutes would be tight including buying a ticket but, if you miss it, you would not have a long wait for the next train.

Where are you looking? There are direct trains from Rome to Napoli Centrale. No changes.
Then you transfer to the local commuter train to Sorrento- Circumvesuviana- which is downstairs, runs frequently (about every 30 min) so you don't need to worry about missing, if you do just take the next one.

It is 2 different train systems. I would just book the Rome to Naples leg with Trenitalia.
https://www.trenitalia.com/content/tcom/en.html

Then get your ticket for Circumvesuviana when you get there. It's just a few euros.
https://www.positano.com/en/naples-to-sorrento-train-schedule?timetable_route=sorrento_napoli

To clarify: Napoli Centrale and Napoli Garibaldi are the same place, for all intents and purposes. They're two parts of the same station complex.
So, it is only one connection, not two.
In other words, if the schedule you see gives you a route such as "Roma Termini - Napoli Centrale - Napoli P. Garibaldi - Sorrento", the time they give between Centrale and Garibaldi is not spent on a train, but walking between the two parts of the station. It is not a particularly long walk, as mentioned by other posters.

It is not possible to reserve seats on the Circumvesuviana, but there is a much less frequent, less .... earthy .... tourist product that uses the same tracks but costs more and many fewer runs. It might even be air conditioned. You don't give the source of the schedules you cite, but I remember that the Circumvesuviana is quite a long (air-conditioned, marble tile floor) walk on the lower level, turning right from the escalators down from the main concourse. If you turn left off the bottom of the escalators, a similar long walk takes you to the paid toilets.

Some people do not realize that the Naples main rail station is newer and better designed than many American train stations. It's not that large, but I agree that it's at least ten minutes from a long-distance train to the Circumvesuviana. As noted, it doesn't matter if you miss a Circumvesuviana standard train. Download a schedule, but remember that this is Southern Italy.

The signage on the Circumvesuviana platforms in Naples is not as good as for the long-distance platforms. A kind local told us we weren't on the train for Sorrento in time for us to jump off. You do buy your ticket from a human, rather than from a nearby tobacconist, as you will in Sorrento. Most tickets have to be validated just before boarding, but I forget if that is true in Naples. Look for machines to do that.

Tim,
The source of the cited schedules in trenitalia web site, if that makes any difference to your response.
Thanks

Trenitalia's site shows the icon of a man walking between the 2 trains.

Frecciarossa XY > WALKING MAN > R CLS XYY
it's two trains and one change. Otherwise they'd list 3 trains and 3 train codes.

Ten minutes is enough if you know where to go, Trenitalia doesn't sell impossible connections. Their hate for passengers hasn't reached such heights, yet. Anyway the shopping area inside Napoli Centrale is on Google Maps' Street view, on a desktop PC you can virtually walk from the surface tracks area through the shopping area and up to the stairs leading to the underground tracks.

Not that missin a local train is a tragedy, you will have to wait for 30 / 45 minutes and take the next Circumvesuviana train headed to Sorrento.

What everyone is trying to say, is that you should be able to book a ticket from Rome to Naples on a fast train, then switch to the commuter Circumvesuvia, for which reservations or tickets are not available (except for maybe the infrequent tourist express trains)

Just focus on the Rome to Naples portion, then go over and catch the first train to Sorrento/

To add to the above, here's the Circumvesuviana schedule (scroll right for full schedule):

https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule?route=napoli_sorrento#section-schedule-result

A few comments to add (I wasn't sure if these were mentioned in one of the other replies).....

You may find this website interesting - https://www.sorrentovibes.com/getting-from-naples-to-sorrento-best-route-2022/

The Circumvesuviana has somewhat of a "colourful reputation" but it is certainly one option to get from Naples to Sorrento. You could also use the Campania Express (mentioned on the above website) - https://www.visitpompeiivesuvius.com/en/campania-express-train-schedule