Hesperia or Elysium seem to work fine as the name of the New World ITTL.
As it concerns Nova Roma, it seems excellent as the name of the US-like polity, I'm somewhat uncertain to use it to name the whole continent(s), it seems a bit...pretentious.
Testudinia seems... weird.![]()
Well the Romans certainly were pretentious enough for that.
Hesperia, IMO, is most plausible, given the association with Roman culture.