The Scots call today, the last day of the year (and particularly the last evening), Hogmanay. The origins of this word are obscure. The Oxford English Dictionary suggests it comes from the Old French aiguillanneuf, and, certainly, France and Scotland were very closely allied at one time (to the 16th century) against the common enemy England, so the Scots may have borrowed this French word. An neuf means 'new year', but no-one is quite sure what the first part of the word refers to, although at one time it was widely believed to refer to mistletoe (gui in French), an idea now discounted by French scholars. Another suggestion mentioned in the OED is that it is a corruption of the Latin calendae, in English 'calends', defined in the dictionary as 'The first day of any month in the Roman calendar', the term being in use until the 17th century, the same century the word Hogmanay was first recorded.
The 16th-century writer Rabelais uses the phrase aller à l'aguillaneuf le premier trou de l'an in Gargantua and Pantagruel (French text here - see page 37). That is translated in the Gutenberg edition as 'to go a-handsel-getting on the first day of the new year' (see here). Handsel is an old word meaning a gift given for the new year, which is designed to bring good luck to the recipient.
A very happy new year to all readers!