Qipchaq was one of the earliest Turkic tribes according to Oghuzkhan epoch. Qipchaq means the cave in the tree in old Turkic (Abulghazi interpretation). One child was born in the cave of the tree, and Oghuzkhan gave him the name of "Qipchaq" and his decendants became Qipchaqs.
Aside from these legend, they were the main Turkic tribal alliance in the western steppe (which was also called deshti-Qipchaq) before the Mongol conquest. According to Hungarians, they also called themselves Kun, maybe the name of the leading tribe (Originally Hun itself is related to Kun, which means Sun in Turkic). The origin of the Coman might be Kunan. According to Qeshqeri, "An" and "En" can be added as suffix to make plural form of the words in old Turkic language, like:
Er + en = Eren ( males)
Oghli + an = Oghlan (sons)
Tur + an= Turan (Tur people)
As for their ethnic composition, they could be a tribal alliences of different groups. However, their leading tribes and language was Turkic (refer to Codex Comanicus).
During Mongol conquest, not all of them moved to the west, many of them intergrated into Jochi ulus, and Golden Horde was also called Qipchaq Khaghanate. Qipchaq is now one of the major Turkic language group including Qazaq, Tatar, Bashqurt etc languages. There is also a clan with the name Qipchaq now among Qazaqs AFAIK.