Assyrians are known to refer to the upper Tigris as Qardu, and the term used by the Muslims to describe the nomads in Iran was kwrt, but the origin is unclear. The Sassanids did used the term to describe them in a letter about Ardashir I defeating them in battle. There have been numerous independent tribes of Kurds throughout history, during the middle ages they did organize in principalities and the have been vassals many times as well, an example of this is Ardalan. Though there hasn't been a Kurdistan, they have been unified under a Kurdish ruler a couple times.

There hasn't been a modern Kurdish state that encompassed the whole population. There was the Median empire, but that's before Kurds became "k-u-r-d." There have also been several small kingdoms, some independent, some semi-independent. They were "Kurdish" as in the ruling family was Kurdish and their populace was mostly Kurdish, but that was the nature of monarchy. Bohtan, Bahdinan among others. Then there were some short-lived Kurdish states like the Republic of Mahabad and Republic of Ararat. Also small pockets of territory, never one encompassing the whole territory of Kurdistan.

The idea that a state should be organized around language/ethnicity is a fairly modern one.