No guarantee obviously, but in a dozen of journeys on Italian trains with such online tickets (for the high-speed trains) I have yet to be asked for a proof of identity. I would not be too concerned about a wrong name, especially if the name still "sounds right" (e.g. not an Asian name for an obviously Italian person).
Also in the internal mailing list of the Italian institution I belong to, at times tickets are being offered for resale when the original purchaser is unable to use them, so safe to assume that it is not unheard of between people who know each other.
That being said, officially the tickets do not seem to be transferable, even when you book the full price "BASE" fare.