If one wants to pronounce this name properly (at least with this spelling), one would have to pronounce the "J" like the French "J." It's not (moj-gaan), it's (mozh-gaan). My mom has the same name, but she writes it as Mozhgan, which makes more sense than using a J given that the name is written with the Persian letter "zhe." Awesome name, though.
My uncle (by marriage) has a sister by this name who spells it Mojgun. She was born in Iran and says it has the same meaning in Persian - "eyelashes" - which I think is really cool because she has the prettiest eyes I've ever seen!