January was named for the Roman god Janus, known as the protector of gates and doorways, and who symbolized beginnings and endings. Janus is depicted with two faces; one looking into the past, the other with the ability to see into the future. The Romans often made promises to Janus and exchanged good wishes.

Janus am I; oldest of potentates;
Forward I look, and backward, and below
I count, as god of avenues and gates,
The years that through my portals come and go.

Henry Wadsworth Longfellow, American poet (1807–82)