The name Mugetsu consists of two Kanji symbols - "mu" and "getsu".
The Kanji "mu" stands for naught, nil, nothing, or non-, un-, dis-, while the Kanji "getsu" stands for moon or month. So, the more-or-less direct translation of "Mugetsu" would be "moonless" - or at least that's how I'd translate it (I'm just an amateur).
The word "Mugetsu" is also a Japanese season word (specifically autumn), meaning "moonless night". It's also used to describe the moon when it's "invisible", covered by clouds.
Here's what Kabalarians have to say about his name:
"Your name of Mugetsu creates an idealistic, sensitive nature and a desire for culture and the refinements of life. You would work best in a relaxed environment at tasks involving writing, mathematical, or analytical skills that require concentration. You appear calm to others, but at times you suffer inwardly with nervous tension. You can find it difficult to express your deeper thoughts and feelings verbally. It is much more natural for you to express your deeper thoughts in writing. A lack of positivity and confidence is a source of difficulty in making decisions in business dealings. You are easily offended, and can suffer with moods of depression. You want the best, but lack the confidence and aggressiveness to materialize your desires. Procrastination is a weakness, for so often you are inclined to avoid issues and to leave things undone until the last moment when you are forced to take action. You are inclined to indulge in rich foods that lack proper nourishment.
This name creates weaknesses in the heart, the respiratory organs, or the kidneys."