I like the sound of it, and there's something fun about Moz as a nickname. The only real problem, I should think, will be people leaving off the first M; even if you're not bad on Ancient Greek spelling the MN- isn't obvious.
I think you need a short MN with it.
Mnemosyne BelleMnemosyne RuthMnemosyne GraceMnemosyne AnnMnemosyne SaraMnemosyne RaineMnemosyne JadeMnemosyne ClaireMnemosyne KayMnemosyne KieraMnemosyne JaneMnemosyne Scarlett (I like this)
Mnemosyne NoorMnemosyne LinaMnemosyne RaeMnemosyne VioletMnemosyne SaraiMnemosyne TamarMnemosyne Mai
Any you like?