Turan is Iranian tribe who was ruled by Iranian ruling class. Saladin most probably Turkic mother who was relation noble Turkic lineage.
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"The rise of the Ayyubids really begins with the exile of Šāḏī from Dvin, perhaps in 524/1130, when a Turkish general seized the town from its Kurdish prince."
http://www.iranicaonline.org/articles/ayyubids
Turan is not a Turkish name. But Tuğtekin, Gökböri names and Khatun titles are turkish/turkic.
The province of Salahaddin in Iraq, which includes the town of Tikrit, was named after him. There is a University of Salahaddin in Erbil. There is the Salahaddin airport in Hakkari. A Kurdish town north of Erbil traditionally called Pirmam has been named Salahaddin in official documents.
He is very much the epitome of Shafi'i Kurdish identity.