Very pretty. I think it's a classy name, and even though it's not uncommon to have heard it before it's still not one that you see every day on a real person. I tend to like fairly 'classic' names, so that's the sort of thing I'd pair it with. Such as:
Monica ElizabethMonica ElaineMonica ConstanceMonica CatherineMonica EleanorMonica TheresaMonica ChristineMonica MarcellineMonica ClarityMonica Davide (I know
Davide is a masculine name, but I met a girl with it once and it was very pretty on her. She said it da-VEED; I don't know the actual Italian pronunciation, though.)
Monica PatriceMonica LaurentineMonica LaurelMonica Frances