A "Moon" is an addition subtype. This card does not refer to cards with the name "Moon" in them.
If there are competing "gain" or "loss" effects, the most recent effects is applied. For example, if Loup-Garou is played while an opponent has a "Fina, the Silver Player" on the field, its gain effect will override Fina's loss effect. However, if Fina is played after Loup-Garou is already on the field, Fina's loss effect will override Loup-Garou's gain effect.