Wikipedia sez
The "nog" part of its name may stem from the word "noggin", a Middle English term used to describe a small, wooden, carved mug used to serve alcohol... Yet another story is that the term derived from the name "egg-and-grog", a common …
Online Etymology Dictionary sez
Noggin: 1620s, "small cup, mug," later "small drink" (1690s), of unknown origin, possibly related to Norfolk dialectal nog "strong ale" (now chiefly in eggnog). Informal meaning "head" first attested 1866 in Amer.Eng.…