And according to the Darius Behishtun...
Column 1:
(1.1-3.) I am Darius the Great King, King of Kings,King in Persia, King of countries, son of Hystaspes, grandson of Arsames, an Achaemenian.
(1.3-6.) Darius the King says: My father was Hystaspes; Hystaspes' father was Arsames; Arsames' father was Ariaramnes; Ariaramnes' father was Teispes;
Teispes' father was Achaemenes.
(1.6-8.) Darius the King says:
For this reason we are called Achaemenians. From long ago we have been noble. From long ago our family had been kings.
(1.8-11.) Darius the King says: there were 8 of our family who were kings before me; I am the ninth; 9 in succession we have been kings.
...Achaemenes was the first "king" of "Persia", right?
(Just getting on track here so bear with me.)