The answer is Janus, the Roman god of doors and gateways! He is depicted in ancient Roman culture as having two faces, one looking back, and one looking forward. In this way, it makes sense that the Romans named January after him, looking back at the old year whilst simultaneously looking forward to the new one.
In his role of Guardian of Exits and Entrances, his image could be seen on many ancient Roman city gates and doors, and in Rome itself there were many temples dedicated to Janus. He also appears on Roman coins, as seen in the picture above, which demonstrates just how important he was in ancient Roman culture.
Although today we don't have a god of doors in our culture, perhaps January might be the best time to get a new door, to create a new entrance and exit, symbolizing the new year ahead and the old year that has passed.
Everyone at Shaker Doors wishes you a very Happy New Year.