I respectfully disagree. Yes, the effects of this new weather condition draw from the idea of a full moon, but "Full Moon" itself just sounds like a boring name. Plus, during a full moon, there is a great deal of light in the sky, despite the fact that it is nighttime and supposed to be dark, hence harsh moonlight. Also, the name draws a parallel to the already existing weather condition, "harsh sunlight". Much like night and day are counterparts to one another, "harsh moonlight" and "harsh sunlight" are supposed to be counterparts to one another.
I recognize that "Lunar Eclipse" and "New Moon" were also among your suggestions, but they are the exact opposite of what this weather condition represents, because a Lunar Eclipse is when the moon is completely blocked out by the sun, and a new moon is when the moon is at its darkest.
Regardless, I sincerely appreciate your feedback.