The claim that the name "Palestine" is a Roman invention is a well-known hasbara propaganda trick. It has just enough truth in it that you can't just say it is a lie, but it has the effect of a lie. The name of the country has been Palestine or a cognate thereof since at least the twelfth century BC, though different languages have varied over the word begins P, Ph or F (which is a quite common linguistic phenomenon). The Romans were therefore not inventing a new name, but reverting to the normal name when they renamed the province "Syria Palaestina" in the 2nd century AD -- it was nothing to do with illegitimately erasing the name of Judea, but rather ending the naming of the province after just one of the peoples who lived there, who had conquered the others and renamed the whole area after themselves before themselves falling to Roman rule.

Over the fourteen hundred years from the twelfth century BC till the Roman renaming in the second century AD, various peoples called part or all of the country "Peleset", [the land of] "the Philistines", "Philistia", "Palashtu", "Palastu", "Pilistu," Palaistinê". By the 5th century BC Herodotus clearly applied the name Palestine to the whole area up to and including the valley of the Jordan. Even Roman Judean writers Philo of Alexandria and Josephus used the term Palestine before the Romans officially changed the name of the province from Judea to Syria Palaestina.

And of course the Arabic name "Filastin" is pronounced very similarly to almost the oldest variant of the name, "Philistine".