Roma / Rome to Lecce by train

ItaliaRail lives up to its name by selling tickets for rail journeys within Italy and the core feature of its service is that it is primarily designed to be used by international visitors to Italy.
So the English translations of place names are used when looking up journeys and the terms and conditions for using each type of ticket are clearly explained.
It also clearly points out the additional costs of upgrading to other classes and types of tickets while spelling out the additional benefits of doing so.

Users of InterRail and Eurail passes can also book seat reservations on the Frecce and InterCity trains without paying a booking fee,

Trenitlalia is the national rail operator in Italy and in addition to its cheaper types of ticket; it also typically offers other discounts available to non-Italians, which include:

• Group Offers, provides for a discount of up to 50% when 3-5 Adults travel together.
• Family Offer for when groups of 2 - 5 people are travelling together and at least one of the party is a aged 11 and under.
• The Children Free Offer is available for journeys by Frecce trains, when groups of 2 - 5 people are travelling together and at least one of the party is a aged 15 and under.
  Those aged 15 and under travel for free, but the Adults will need to purchase full price 'Base' tickets.