Janus is depicted as 2-headed or 4-headed Roman God. Somewhere I had read that she was the Goddess of Learning, but when I went to Wikipedia to confirm, I could not find it. Then why they have it as a girl's name?
Back of my mind, I have always associated "Janus" with God of Knowledge and Learning, and am not sure why exactly, unless the subconscious mind is playing tricks!
The connection with Ganesa just happened to me now when I reading another book, where his depiction is mentioned, when talking about a certain iconography of Gnostics.
So lord Ganesh in India is associated with Knowledge and Learning and he is depicted to be the one who transcribed the 4 Vedas, the most ancient and the earliest known books of knowledge from India, and declared by United Nations to be an Inheritance of Humanity.
Ganes can be written as "Gna" + "Ish", which means, Lord or God of Knowledge. Some people say "Gana" + "Ish", meaning Lord of Masses or Leader of Masses. But who can be the Lord of Masses unless he is Intellect, Knowledge and Wisdom wise wiser than the Masses?
Now why Janus would be depicted with 4 or 2 heads? Is it to show his possession of more knowledge and intelligence? Or his lordship over knowledge and intelligence? He is portrait as someone who can go forward and backward in Time.
Now they say the true knowledge is that knowledge that takes you across space and time, and makes you eternal, e.g. the knowledge of Brahman (Super Soul) or Atman (Individual) Soul. The rest of the knowledge is a subjective and man-made knowledge. The true knowledge makes you transcend the cycle of Birth and Death, and free yourself from the shackles of Life and its associated Sorrows and Joys, which is rare and subjective anyway. It is about the identification of oneself to what essence of the Self. Is it Body, Senses, Mind, Ego, or Intellect? All these identifications and anchoring oneself only makes one subject to the travesties of Death and Life, and of Joy and Sorrows. But the identification that you are "Atama", Atom, or part and parcel of the Supreme Self, and because He is always there, you are always living! Alas, you have conquered Death and gained Immortality!
It is for that reason why an intelligent person like Ravana of Ramayana is shown with 10 Heads.
So maybe Janus is shown for the same reasons having 2 or 4 heads.
"J" and "G" are interchangeable, and "gna", "jan" and "gno" are same.