[narfforc]

I have over forty copies of LotR, and in every one the name Rhun appears to the east of The Sea of Rhun. In Fosters Guide to Middle-Earth under the heading Rhun it states thus:
Rhun (S:'East') Name given by the Dunedain of Gondor to the area east of THE SEA OF RHUN.

The East-Lands up to and including The Sea of Rhun were ruled by Gondor under Turambar, and these lands returned to the crown under The Reunited Kingdom. If you wish to be pedantic you could say that the northern end of the lands known as Rhun, would be Northeast of Mordor, in the same way many Londoners think people from Birmingham are Northerners or to the extreme, how some of our American cousins think Scotland is an area of England.