Love this skeletal, wavy handwriting! 月光荘 is read Gekkōsō. Breaking it down:
月光 [げっこう] means moonbeam or moonlight.
月 means month or moon. It’s read つき, ゲツ, or ガツ.
光 means light or ray. It's read ひか.る, ひかり, or コウ.
荘 means villa, inn, cottage, feudal manor, solemn, or dignified. It often shows up as a suffix in hotel or business names, conveying a sense of luxury or dignity. It's also the counter for games of Mahjong, in which case it's read チャン. Otherwise, it's usually read ソウ or ショウ, rarely ほうき or おごそ.か.