[thaumasiotes]

> but it was still the language used for diplomatic purposes as far away as the Aegean Sea and the Egyptian imperial court.

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.