The name Janus is a boy's name of Greek origin meaning "gateway". Janus and is often added to lists like Mythological Baby Names for Boys and discussed in our forums with posts like "Hunt for our favourite boy names (Alphabet-wise)".
From the experts:
The meaning of this ancient Roman god's name relates to transitions, hence its connection to the name of the first month of the new year, a time of fresh beginnings. Janus is usually depicted as a two-faced god facing in opposite directions, since he looks both to the future and the past. The Slavic form Janusz is more commonly used than the English, represented by the Polish cinematographer Janusz Kaminski, who has shot all of Steven Spielberg's films from Schindler's List to Lincoln.
But with January having been taken over by the girls, why not consider Janus? One caveat: it does sound a lot like the female Janice.