Janus, the Roman god of beginnings and transitions, gave January its name.
Janus was traditionally depicted with two faces, one looking forward and one looking backward. That image made the god a fitting symbol for the transition from an old year to a new one. The Latin name Ianuarius became the source of the English word January.
Roman religious tradition associated Janus with doors, gates, passages and changes. His role was broader than New Year's celebrations alone, but the symbolism of looking in two directions made him especially relevant to the start of a calendar year. January was named for him because it was understood as a threshold month.
Janus is sometimes mistakenly described as a god of time in the same way as a clock deity. His central idea was transition and beginnings. The two faces represent different directions or states, not a claim that he literally controlled the future and past.