Kunta Kinte was a member of the Mankinka tribe of The Gambia in Africa c. 1750. The Mandinka-English dictionary published by the Peace Corps ( 1995, The Gambia) shows these meanings: Kunta (as a noun) a man's name or surname and kunta (as a verb) to fit (as in "does it fit in the box?")
The words Kuni, Kunindi, and kuninta may possibly be words from which "Kunta" derived. They all are variations on a theme meaning to awaken, be awake, or to be aware. Derivation of the name Kunta from these words is only a guess on my part, however. The word Kinte is not listed; we assume it was the family surname.