January is named for Janus, Rome's two-faced god of gates. The Renaissance poets loved this idea, and often used Janus, who looked backward and forward at once, as an emblem of their own vocations. Here's Edmund Spenser, from his 'Amoretti' sonnet sequence (1595), describing the emergence of a new year from the gate of the old.
New year forth looking out of Janus' gate,
Doth seem to promise hope of new delight:
And bidding th' old Adieu, his passed date
Bids all old thoughts to die in dumpish sprite.
And calling forth out of sad Winter's night,
Fresh love, that long hath slept in cheerless bower:
Wills him awake, and soon about him dight
His wanton wings and darts of deadly power.
For lusty spring now in his timely hour,
Is ready to come forth him to receive;
And warns the Earth with diverse colored flower,
To deck herself, and her fair mantle weave.
Then you fair flower, in whom fresh youth doth rain,
Prepare yourself new love to entertain.