Can someone help orrrr?

Mackenna

On my birth certificate it says "Gemini/Sagittarius" that's impossible though now look at my birthstone necklace

I am born on December 15 so there's no way I'm a Gemini BUT my moon sign is "full moon" which means Gemini. Gemini is May21-June21 idek if this is rare or if there's some mistake? I just really hope someone helps. (Btw time of birth is 3:21 pm) invade that helps.