月影 (つきかげ・tsukikage) is a word that means 'moonlight' and is made of moon + shadow kanji.
The reverse order of the kanji, 影月 (かげづき・kagezuki) doesn't appear to be a word, which makes it reasonable for a made up name.
陰 means shadow, but also has a sense of 'in secret'.
蔭 is rarely if ever used now, but probably had the same meaning as 陰.
翳 as a character is used in かざす (to hold up to), so it's not a completely obscure kanji. It shares a dictionary entry with 陰, but I've never seen it used for かげ.
景 shares a dictionary entry with 影, but I've never seen it used for かげ. It's more known as けい meaning scene/view in compounds like 風景 and as a suffix.