Boo,
Moon,
Moonlight,
Moony,
Clay,
Circle Guard,
Circle,
Mumma,
Papa,
Mum,

And with her being called Boo, she has a twin with the matching name, her twin is Ran. Her opposite, but it's not twin as in twin sister or brother, it's as in twin lover, so her lover designed Ran and is now sometimes known as Ran, Boo's lover,

Welllllll she's actually know as a few names wich give hints of what she is, Here are the names