Janus gave January its name and was associated with beginnings, transitions, and doorways.
Roman tradition pictured Janus with two faces, allowing him to look forward and backward. That image made him an appropriate symbol for the transition from one year to the next. The Latin month name Ianuarius became January in English.
The Roman calendar’s New Year date changed over time, but January 1 eventually became the civic starting point in the Roman world. The month’s association with Janus is why January is especially linked with new beginnings in later European culture.
Janus is sometimes confused with Saturn because Saturnalia was a major Roman festival in December. Saturn was a different deity, associated with agriculture and time in Roman religious tradition; he did not give January its name.