Note: In sequences of /nk/ the /n/ is barely heard and the /k/ becomes voiced to /g/. The word is therefore heard as /gamwin/.
From Proto-Algonquian *nekamowa he sings. Also cognate is Narragansett Nickómmo "a Feast" "After Harvest, after hunting, ... especially in Winter" (Roger Williams, Key, 1936:127), and Meskwaki - nakamowa he sings a religious song. (comment by Ives Goddard)