At both new and full moons (lunar phases) the tides are most pronounced (for example, the highest high tides).
I think it might be called the "tail." I might be getting this mixed up with a comet, but I THINK(emphasis on think ^^') they're similar in that aspect?? Sorry if this didn't help.
In fact, since the Moon is constantly rotating on it's own axis, there is no area of the planetoid which is permanent darkness, and the far side of the Moon is only completely devoid of sunlight during a Full Moon - when the Sun is facing the Moon with the Earth in between.