Herodotus used the word Palestine for the area where the Phillistines had lived, since the only area he had visited was the coastal area.
LOUIS H. FELDMAN, Some Observations on the Name of Palestine, Hebrew Union College Annual, Vol. 61 (1990), pp. 1-23
www.jstor.org
The Romans, on the other hand, joined the Provinces of Judea and Syria together after Bar Kochba so that the Jews would stop their riots and forget about their homeland.
They used the word Palestinea because of the Philistines who had defeated Israel, during that time in order to humiliate the Jews.
It did not work about the Jews forgetting their homeland and wanting to have sovereignty over it again.
In other words, up until the Romans decided to humiliate the Jews in 135 AD, the Jewish homeland was called Judea/Judah, by the Assyrians, the Greeks, and the Romans .
Judah was the Jewish Kingdom which survived the Assyrian invasion which scattered the Kingdom of Israel. The 10 tribes.
Which is why I asked you what part of the area did Herodotus call Palestine in the 6th century BC, which he clearly had called that after the Philistines who lived in that small area.