Middle English: Januarie
Latin: Ianuarius (of Janus)
Latin: Ianu(s) (Janus)
Latin: Ianuarius (pertaining to Janus)
Latin: Ianuarius mensis (month of Janus)
Januarius had 29 days in the Roman calender, with Julius it became 31 days long.
Ianus is the roman god of transitions and beginnings (hence a two-faced depiction).