January was formerly called Januarius and is named after the Roman god Janus (pronounced "JAY-nis" or "JAH-nus"). In Roman times January was the eleventh month, but Janus is the perfect namesake for the beginning of the year. He is the god of gateways, doors, beginnings, endings, prophecy, and time. He usually appears as having two heads facing in different directions. This is so he can see into the future and the past. He married and had many children, including his son Tiberinus, a river god who the Tiber River is named after.
Janus played a big role in the story of the founding of Rome. Romulus and his fellow men realized that there were no women in their new city, so they went to the neighboring city of Sabine and abducted some of theirs. When the Sabines attacked Rome in retaliation, Janus released a burst of volcanic hot spring water. This killed, maimed, or deformed many Sabine men, and they retreated. Evedently, at this point the Sabine women liked being Roman, but that's a whole other story.
According to legend, Romulus admired the god's power so much that he created the tradition of the Janus. The Janus was a walled, roofless structure with a big gate that was left open during wartime. This was so the god could help them out at any time. The doors were left closed during times of peace, which didn't happen very often.
Several historians have suggested that Janus was the most important deity to the Romans and was often invoked along with Jupiter. I find this surprising since I don't remember him ever being mentioned when I was a child reading books about Roman mythology. It's weird that almost everyone has forgotten about him.
Here's the biggest challenge with this name that I'm sure some of you have noticed already: it sounds like Janice. In fact, until a while ago, I thought Janus was just another spelling for Janice, and that the god was a goddess. This is the risk of names that clash with gender assumptions. Even if they're legitimate masculine names, sheer unfamiliarity is going to cause people to stumble. That might be why Janus, while used on occasion, is still a rare name. January is also a name option for both boys and girls that, while not popular yet, I hear a lot more. Whichever one is picked, you'll be honoring the same guy.
Sources:
http://en.wikipedia.org/wiki/Janus
http://www.pantheon.org/articles/j/janus.html
http://www.babynamewizard.com/namipedia/boy/janus
