What are the mythological names of the two sundogs?
I have no idea. Sundogs are reflections of the Sun in high-altitude clouds, usually containing ice crystals. They are commonly seen in the Fall and Winter months on afternoons when storm fronts are passing through with upper-level cirrus cloud decks. These ‘mock Suns’ can be very dramatic, but seldom looking like circular disks themselves. Instead, the ones I have seen in the Washington DC area look like irregular patches of light seen against a cloud about 30-40 degrees from the Sun. Sometimes they show a rainbow coloration. In the arctic regions, sundogs are very common as are other even more striking spectacles caused by sunlight refracted into rings, arcs and multiple sundogs over much of the sky.