Eurail and Rome to Naples train

First mistake, buying a Eurail Pass. But I guess its a done deal. Yes, of course you can buy tickets for the Rome-Naples train. That is how 99% of the people ride the trains in Europe.

How far ahead is just a matter of how much you want to save. Train tickets are sold like airline tickets these days. Buy a nonrefundable ticket months in advance and save 50% or more. Wait till the last minute and pay full fare. Trains are rarely completely full except maybe Easter weekend going to Rome. And when you buy a ticket, it includes seat reservations which you pay extra for with a Eurail Pass. You also have the option of two railway companies on the main routes, Trenitalia, the national railway, and Italotreno, a private operator. Both operate high-speed trains on the Naples-Rome line. Some people prefer Italotreno and sometimes their prices are better than Trenitalia.
Use something like www.thetrainline.com or www.loco2.com. They sell tickets for both at the same price as direct with fewer credit card verification headaches. But start by looking at the prices and schedules at https://www.trenitalia.com/en.html and www.italotreno.com. And use Italian city names, Roma and Napoli.

Sam's advice is correct. You can either purchase at the station the day you wish to travel, or go ahead and purchase if you know your schedule (to save money). I'm seeing prices for the fast trains at 48 euros tomorrow or 19 on June 11th, 2019. So you can save if you go ahead and book but, it will be non refundable and for a specific train. So yes you can purchase separately (train station or online using the links Sam provided above) and they appear to be available now.
Good Luck and I hope you have a great trip!

Is this the shortest/cheapest trip among your 6 travel days? You can spread out the 5 covered pass travel days as you wish within a one-month window. Nobody will know or care which days you choose to buy separate tickets, so it need not be the last day.