Eggnog literally means eggs inside a small cup. It is used as a toast to one’s health. Nog is an old English dialect word (from East Anglia) of obscure origins that was used to describe a kind of strong beer (hence noggin). It is first recorded in the seventeenth century. Eggnog, however, is first mentioned in the early nineteenth century but seems to have been popular on both sides of the Atlantic at that time. An alternative British name was egg flip. The reason you won’t find 16th century recipes for “egg nog” is the term didn’t appear in print until the next century.
Eggnog goes by the name coquito in Puerto Rico, where, not surprisingly, rum is the liquor of choice. Mexican eggnog, known as rompope, was created in the convent of Santa Clara in the state of Puebla. The basic recipe is augmented with a heavy dose of Mexican cinnamon and rum or grain alcohol, and the resulting drink is sipped as a liqueur. In Peru, holidays are celebrated with a biblia con pisco, an eggnog made with the Peruvian pomace brandy called pisco. The Germans make a eggnog or rather egg soup with beer (Biersuppe).