I should apologise for being somewhat vague in my title, but this is a topic of great confusion for me. I say Persian, rather than Iranian to specifically avoid the Medians, though I understand it might be impossible as they were something of a hegemon.
King Kuras of Parsua/Parsuwash/Parsumash has been identified as Cyrus I of Anshan. My understanding is that there are two views: first, that Anshan and Parsua are the same; and second, that Parsua was a separate kingdom somewhere around Lake Urmia, from which they migrated to Anshan. This is a great source of confusion for me.
What are the sources for Parsua/Parsumash? Is it simply the Akkadian reading of Parsa, or is it a separate name for a separate region?
Is there any consensus on the location on this kingdom, i.e. whether it is synonymous with Anshan? Because Old Persian cuneiform was not recorded until the Behistun inscription, could it be that references to 'Anshan' in the Cyrus Cylinder were references to a Persian kingdom, using a name familiar to Babylonians (for the same reason as he had paid tribute to Marduk)?
Is the only source of the Teispids being kings of Anshan the Cyrus Cylinder? Could it not be interpreted that Cyrus' progenitors were merely the chiefs of his clan, and Cyrus said Anshan for the sake of simplicity, or out of ignorance?
If Parsua has an Iranian etymology and the Teispids were Kings of this land, wouldn't that support the view that Cyrus II was Iranian rather than Elamite?
I apologise if I have made any false assumptions, I am by no means a historian. Please feel free to correct me. It just seems that there is so much contradicting information on this topic, and sources are few and far between. Thanks for reading, and I would greatly appreciate any responses.
That is a very complicated question. The Encyclopedia Iranica is a great, peer-reviewed source but I would also recommend having a look at Amélie Kuhrt's The Persian Empire: A Corpus of Sources (2007) and the article:
To try to answer your four questions:
The big advantage of this view is that it relies on what Cyrus and his contemporaries wrote, not on what we think they should have written.
No, a cylinder seal is labeled "Cyrus the Anshanite, son of Teispes" in Elamite (although this seal was used in Darius' day, so it may be just another Cyrus and Teispes not two kings) and the Nabonidus Chronicle from Babylonia says that "Cyrus, king of Anšan" defeated Astyages the king of the Medes.
No. After all, England, Wales, and Aquitaine had etymologies in three different language families, but one family of Angevin kings and queens! And most people in Massachusetts or Pennsylvania do not identify as Wampanoag or Latins, despite their lands having Wampanoag and Latin names.