The word Palestine is the Greek word for the Hebrew word invader. The so called Palestinians you try to jump through hoops for, were Greek sea people who occupied, briefly, a coastal strip around Gaza. Herodotus, who never visited the area, was a pretty rotten geographer and historian- something we learn in grade 6 or 7. Still, it doesn't matter what the Greeks called it, or what the later Romans called it to erase the Jewish identiy- it matters what the local people called it, and it sure wasn't Palestine to them 2000 years ago. The whole Hannukah story is armed rebellion to drive out the Greeks and foe Jewish self-determination in their own land.

As for more modern times, the Palestinian football team famously toured Australia- all Jews. The Palestine Post, later the Jerusalem Post, was a Jewish publication. The coins used during the mandate period that say Palestine, also have in Hebrew Eretz Yisrael- the land of Israel, on them in Hebrew. Jews were relatively happy to be called Palestinian, but Arabs saw it as an affront and Zionist propaganda and rejected the term, stating they were not Palestinian but South Syrian or Jordanian etc. The term Palestinian to describe the Arabs of the area started adoption 1964 and became official in 1967.

So, yes, the term Palestine is an ancient one, to describe an invading people that no longer exist and later a name by colonial powers to erase the identity of those who lived there.

The idea of Arabs of the area adopting it to identify as such, came decades after Israel was re-created.