Kurdistan as a phenomenon in Ilkhan’s Era and its association to historical geography of Iran

Kurdistan has been paid attention to researchers as a part of history of Iran. According to what is mentioned, the first time the word ‘Kurdistan’ had been accepted during the Saljuq dynasty era. According to that belief, king Sanjar made this name common in official places and papers while he created a region called Kurdistan and appointed his nephew king Solomon as ruling. If we accept that belief the problem arises here in the absent place of that evolution in Saljuq era. So the question is what changes has happened to Kurdistan name in public and official. According to original source and texts what was the exact time for these changes?
It seems that this name is closely with Iran in the recent revival of popularity and recognition of Kurdish Ilkhans and time associated with changes Ilkhans government. However this paper issues with help of Critical study historical texts and research conducted as well as a descriptive and analytical practices and techniques common in historical research, recently response to questions and hypotheses that have been proposed to assess.