Tolkien used various “teeth” words related to the root √NAK “bite” throughout his life. The earliest of these was G. naith “a tooth” from the Gnomish Lexicon of the 1910s, where its connection to the early root ᴱ√NAKA “bite” was made more clear by its archaic plural form nacthin (GL/59). In The Etymologies of the 1930s Tolkien had N. naes derived from primitive ᴹ✶nakse under the root ᴹ√NAK “bite” (EtyAC/NAK). As suggested by David Salo (GL/275), another variant ✱nagol “tooth” is suggested by the class plural naglath in the names from Lord of the Rings drafts of 1940s: Naglath Morn “Teeth of Mordor” (WR/122) and Kirith Naglath “Cleft of the Teeth” (WR/137), neither of which made it into the published version.
Neo-Sindarin: For purposes of Neo-Sindarin, I’d recommend using N. nêl or N. neleg for “tooth” words. Primitive ᴹ✶nakse would likely produce ✱nach rather than naes under Sindarin’s phonetic rules; compare S. ach “neck” < ✶aks[e] (PE17/92). As for N. nagol, it was also likely abandoned.