You need to study Bronze age history more. Palestine referred to land along the cost that was occupied by the Philistines. The Greeks had extensive dealing with the Sea People, but little to no dealings with the Jews of Israel, so it is not surprising that they might refer to areas improperly as Herodotus did...

But with Alexander's conquest any confusion was rectified and the area and referred to as Judea (the Greek adaptation of the word Judah).

Historically, both the kingdoms of Israel and Judah roughly corresponded to the area of the West Bank, encompassing Jerusalem, while the coastal region around Gaza, Ashkelon, and Ashdod was associated with the Philistines.

"In coins minted in the Hellenistic era, Palestine was never used to describe the area, though the name continued to be used by many Greco-Roman writers to describe the broader region between Syria and Egypt, most likely because Herodotus by then had long since entered the classical literary canon, and so, his geographical designations continued to carry sway.".. but note, this use of term to describe the area outside of "land of the Philistines" was not considered a proper legal name and not used in any official capacity by those living there until Rome adapted it 100 years after Jesus died.