They were called Mandatory Palestine as that label existed from ancient times. The label applied to all religions of people there including Jews. After 1948 it has applied only to Muslims and Christians. Even if you consider the origins of the identity to be 1964 when the PLO was formed, its still been 3 generations of people?Not really.
Before the Brits took over in 1919, the Palestinians were just generic Arab underlings of the Ottoman Turks, just like the Syrian, Lebanese, Iraqi and Jordanian Arabs. It was the Brits who named and created Palestine - which then included Jordan. The Brits did that, just so they could draw a line on the map and separate British "Palestine" from French "Syria". Both were artificial concepts.