The etymology of the goddess chAmuNDA has mystified old &modern scholars alike. The great mantravAdin bhAskararAya correctly realized that it might stem from some local (non-Aryan) tongue.
Within the Sanskrit tradition the paurANika-s have attempted to give it various functional explanations within the context of the battles fought by the goddess. While the most prevalent one is in mahAsaravatI cycle relating to the killing of chaNDa and muNDa -> chAmuNDA there are alternative versions.
One such is in the kAlarAtrI cycle (e.g. varAhapurANa), where she gets the title from charma-muNDA-> chAmuNDA. The goddess of the kAlAratrI cycle remains considerably popular in the chera country.
देवी च त्रिशिखेनाजौ
तं दैत्यं समताड्यत् ।
तया तु ताडितान्तस्य
दैत्यस्य शुभलोचने ।
चर्म-मुण्डे उभे सम्यक्
पृथग्भूते बभूवतुः ॥ ९५.३० ॥रुरोस् तु दान-वेन्द्रस्य
चर्ममुण्डे क्षणाद् यतः ।
अपहृत्याहरद् देवी
चामुण्डा तेन साभवत् ॥ ९५.३१ ॥
However, the acquisition of the name chAmuNDA probably happened along with the absorption of a old Indian hunter-gatherer goddess into the transfunctional IE goddess sometime after the epic period but very early in the paurANika tradition. Subsequently the authors tried to etymologize the name in different ways.
It is conceivable the core the famous nAvArNa mantra with its peculiar second bhakti was itself acquired as is from the pre-IE tribal tradition. We cannot rule out that the name chaNDikA is another “paralogous” Sanskritization of such a name.