The Roman god who gives January its name is Janus.
January comes from the Latin name Ianuarius, meaning the month of Janus. Janus was associated with beginnings, transitions, doorways, gates, and passages. Artistic representations often show him with two faces, symbolizing a view toward the past and the future, which made him an apt figure for the start of a year.
The early Roman calendar did not always begin in January. March was originally the first month in the traditional Roman system, but January became the opening month by the late second century BCE. The Julian calendar reforms of 46 BCE helped establish the calendar structure that influenced later European systems.
The modern Gregorian calendar retains January as its first month. Janus is not the same deity as Saturn, who was honored at Saturnalia, a separate Roman festival held in December and not equivalent to New Year's Eve.