Disputed. The initial -kur- is obviously Kurd, but theories vary on the -manc- part. Chyet considers it to be a modern Kurdish equivalent of Mede, this falls in line with Kurdish sound changes as in *Mād ("Mede") > *mānd (n-extension before d/t/č/c sounds; as in tanc, derence, fersend...) > mānc (as in gazind > dialectal gazinc); Kurd-Mede. However in Zand-i Wahman yasn, a Middle Persian text, the word /karmān/ is used together and synonymously with /kurd/, apparently connected to Kurmanc, Kerman and Kermanshah. Might originally be the name of a tribe, compare Kirmal and Kirmancekiman (subdialect of Leki).
kurmanc ?
While it is now only used by Kurds in Turkey, Syria and Caucasia (=Kurds of Northern Euphrates); Kurmanc used to be the name for the speakers of all Kurdish languages and "Kurd" was used for the pastoral, nomadic nobility; or used by surrounding groups to differentiate themselves from them (Zazaki Kird, Kirdkî and Kirdas, Kirdaskî). This falls in line with the theory that "Kurd" originally or at some point meant "nomad". 19th century Kurdish rebel leaders often expressed annoyance to the Ottomans lumping them in the same group as the Kurmanj, and often considered sedentary Kurds to be gawir (heathen, pagan) and referred to them as Goran (*gewran; heathens, pagans). The Soran tribe referred to themselves as Kurdekan ("the Kurds"), the sedentary Kurds under them as Kirmac and Hewrami speakers as Goran (hence Gurani). Melayê Cizîrî uses Mîr û Kurmanc ("king and Kurmanj") to refer to the noblemen and their warriors having taken a battle position which demonstrates that Kurmanj isn't considered to be a nobleman but a lower class of which the tribal forces are gathered from for battle. The usage changed after the 19th century when Kurdish nobility (mirs, begs, etc.) was eradicated after the Ottomans ended Kurdish principalities. Some Southern Kurdish speakers have preserved the title of Kurmanj while others have not. While presently only Northern Kurdish (called Badinani by outsiders) is called Kurmanji, it only disappeared after the 70s in the rest of Kurdistan. It is now quite rare in Iraq and Iran and in much rarer forms such as kurdmanc, kirmanc, kirmac, kumanc, kirman, kurman, etc.