I trace the Qıpçaq name to the ancient Turkic tribe of the Quyu (屈庾) or Qushi (屈射):
Quyu (屈庾) LH *k(ʰ)ut-jo < OC *kut-loʔ - Shiji
Qushi (屈射) LH *k(ʰ)ut-źak < OC *kut-mlak – Hanshu
According to them, their name was connected to Middle Turkic *qovuq (قُوُق) “hollow” and *jɨɣɑːt͡ʃ (يغاَج) “tree.” Clauson (1972) cites quv ağaç or “hollow tree.” I derive their name from Turkic *kubɑː “pale, pale Yellow or gray” and the nominal suffix *-t͡ʃɑk. The name likely referred to their horses. Given, it was common practice to name a tribe after a characteristic of its horses. According to Academia Sinica, the Qıpçaq of Bağatur Darğa’s time inhabited the areas around the Yenisey river, just above the Qırğır.
Sometime during or after 203 B.C.E., the Xuŋa, led by Bağatur Darğa, conquered the Qıpçaq, Qırğır, Tägäräk, Hun-yu, and the Sır.