https://israelforever.org/state/Mandate_for_Palestine_Jewish_State/
Mandatory Palestine was what that map calls “Jewish Palestine”, not Trans-Jordan. Note that Trans-Jordan was explicitly not included.
Earlier in my travels, I worked two contracts in Israel. On the local TV channel from Jordan, the "weather map" showed all as Transjordan.
Looking back to maps from the Roman times, the area is termed Palestina. Under the Turks at one time, it was called the Ottoman empire. "Palestine" as an Arabic name is not correct anyway, because of the consonants. So the media construct of today stems from the "Nabka" forward.
That so-called Palestinian flag? It's as almost as new as the LGBT+ flag....