The Roman Emperor Hadrian named biblical Israel “Palestine” in 100 AD to further infuriate the Jews. It was based on the Philistines. The old antagonists of the Israelites.It's an Italian word.
The Greek historian Herodotus in the fifth century B.C. has the word
Palaistine for a portion of Syria (probably the area of the ancient Philistines but it isn't clear what the borders were). Since the name is from the Philistines it must have been remembered through the centuries--that was during the period of Persian rule but I don't know if there is any evidence from Assyrian or Babylonian records of what they called that area.
The Philistines seem to have come from the Aegean area about the same time as the Israelite invasion across the Jordan. They are one of the Sea Peoples mentioned in Egyptian records as "Peleset."