During the time of the British Mandate, who opposed the term "Hashemite Kingdom of Palestine" and who if any were OK with it being called that?

Question

During the time of the British Mandate, who in the British Government opposed the term "Hashemite Kingdom Of Palestine"?

" the Hashemite Kingdom of Palestine. This was the name that King Abdullah (the first) wanted to call his Kingdom after it was separated......The British had given the Jewish authorities an ultimatum — either accept the loss of the East Bank to the Hashemites or risk losing the rights to a homeland (a state) on any of the territory west of the river. The Zionist leadership relented. Thus, the Hashemite Kingdom of Palestine was created. However the British had one caveat for the Hashemite ruler. They advised him not to name his kingdom with the designation of Palestine. Instead, they advised him to call his new kingdom with the purely geographic designation of Transjordan — later to be shortened to simply Jordan.

]The British didn’t want the Hashemites to be challenged by Arabs living west of the river. These Arabs (to the west of the river) had no particular rights under international law other than to live under eventual Jewish sovereignty. In other words, under the revised Mandate for Palestine, there was to be a Jewish state west of the river and a Hashemite Kingdom east of the river." TimesOfIsrael

Answer 1

The more I look into this, the more I doubt whether this blog post by Steven Horowitz is historically accurate on this particular detail.

I can find very few references to the "Hashemite Kingdom of Palestine" anywhere and none of them seems to connect to what Horowitz is saying. Abdullah I officially created the emirate of Transjordan in April 1921. Shortly before this he discussed his territorial ambitions with Winston Churchill, then Secretary of State for the Colonies. Abdullah expressed concern about the rising Jewish presence and Churchill downplayed this. Abdullah made it clear that he wished to rule over all of mandatory Palestine, and Churchill rejected this. The Churchill White Paper followed shortly thereafter. Frederick Peake led the Arab Legion that supported Abdullah's rule.

So, it is true that the British supported Hashemite rule over only the eastern half of their regional mandate, but I cannot find any record of Churchill or anyone else telling Abdullah what to name his kingdom.