What we see as the current and modern state of Israel - did not exist prior to 1948 (going all the way back to ancient Israel - which was completely obliterated and destroyed by the Romans).
In fact, before Ben Gurion announced it - no one even knew what the modern Jewish State was going to be called. Even the “insiders” didn’t know what it was going to be called. Even on Presodent Truman’s official recognition of the State of Israel, you can see the previous typed name scratched out and the “given name” scribbled on that official piece of paper.
So, prior to 1948, it was entirely appropriate for all those people there to call themselves - exactly as they did call themselves - Palestinian Jews and Palestinian Arabs.
The Jews changed their name, when they got their state and the Palestinian Arabs simply dropped the “Arab” part after the Jews abandoned their previous designation.
Those are the simple facts of history, no matter whether it works with someone else’s “narrative” or it works against their “narrative.”
No, that was not the case. It was always outsiders that used the “Palestine” terminology, especially the League of Nations. The Ottoman Empire called the region “Southern Syria” before that.
Even the League of Nations recognized separate countries for the nations living in “Mandatory Palestine”. Everybody knew that the Jews wanted to call the land “Eretz Yisrael” even before Ben Gurion’s announcement, which the League of Nations already knew and even announced.