Actually, Jordan was seperately administered by Abdullah from the start as the autonomous region of the Transjordan. Afterwards, by retaining the name Jordan rather than becoming Palestine the Kingdom illustrated that it did not claim Israeli territory and was not a seperate homeland for the Palestinians either, and so maintained unusually freidnly relationships with Israel.
Of course, it was a bit more complicated. From 1948 till 1967 Hussein I attempted to unify the country's inhabitants by utilising the policy that 'Jordan is Palestine and Palestine is Jordan', trying to persuade people that despite the longstanding division the existence of the state of Israel was a fact that had to be accepted, and so Jordan was the next best thing to a unified Palestinian republic, and as Jordan would be under the Hashemites. After 1967 Hussein increasingly moved to a 'Jordan is Jordan and Palestine is Palestine' due to Israeli attempts to push 'Jordan is Palestine' by urging the Palestinians to revolt and declare their republic in Jordan, thus allowing Israel to claim that they didn't need to evacuate the West Bank as an independent Palestinian homeland already existed. Hussein meanwhile was moving rapidly to offering the West Bank as a heavily autonomous region within Jordan, before eventually, and somewhat reluctantly, giving his claims to the PLO and washing his hands of the whole matter with a somewhat pointed remark to Israel that they had managed to force the one state that they would have been able to openly negotiate with out of the equation.