Upvote:2
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.