I have to wonder, what primary sources there could be. I would be amazed if there were any.
And also the language in general use in southern Mesopotamia, presumably subject to historical changes.
Note that while the various states in that region didn't call themselves "the Akkadians", they did tend to claim the title by giving their king the very traditional royal honor "King of Sumer and Akkad". By the twelfth century BC, the title was attached to Babylon.