In the Irish there are two versions of Mary - one for Our Lady and the other for ordinary use. Muire and Maire (and there are spelling variations of both.)
I suppose it's some misplaced embarassment about the name that has knocked it out of common use these last couple of generations, after centuries during which it was by far the most common girl's name in England and in America, among Protestants just as much as among Catholics, in spite of everything.
Perhaps people worry that if she's called Mary, any deviltry she gets up to will be a little bit worse. The way you don't get Jesus much as a common boys name in English.
Onhe thing I predict with certainty is that Mary is going to be a common enough name again in time.