Sean Durkin was looking for an unknown actress to play the role of Martha, which was the only role auditions were held for. Elizabeth Olsen auditioned twice for the role of Martha, and had to begin filming only two weeks after winning the part.
Elizabeth Olsen and Sarah Paulson invented together some background for the sisters' relationship. So every scene when they talked about their past, although it's vague on the script and for the viewer, Olsen and Paulson knew exactly what Martha and Lucy are talking about.
There are several references to the work of singer-songwriter, Jackson C. Frank. John Hawkes plays "Marcy's song" in the film, while "Marlene" is played over the credits. It can be assumed that John Hawkes' character, Patrick, fabricated the names Marcy May and Marlene from these songs.
The trivia items below may give away important plot points.
There are quite a few similarities between Patrick's cult or Martha's story in this movie and the real-life Charles Manson "family" group. Among them: Manson, like Patrick, attracted a group of young and attractive but damaged young men and especially women to a remote, rural compound. Manson often renamed the members of his family--just as Patrick decided that Martha should be named "Marcy May," Manson dubbed Susan Atkins "Sadie Mae Glutz." Manson, like Patrick, had sex with all or nearly all of the women a requirement of "family" membership, and both the real Manson and the fictional Patrick encouraged everyone to have multiple sexual partners. Manson murderer Susan Atkins had experienced the early death of her mother and subsequently started having behavioral problems that made her vulnerable to the cult's allure, as Martha had, and Manson murderer Patricia Krenwinkel fled to a relative's home after the murders because she was scared the "family" would track her down, as Martha did. Manson, like Patrick, had his more trusted members go out of the compound at night to break into wealthy people's homes, steal from them, disrupt and terrorize their lives, and ultimately kill some of them.
The title refers to three of the names that the main character is known by over the course of the movie. "Martha" is the first name that her parents gave her. "Marcy May" is the name that Patrick gives her when she first enters the cult. "Marlene" is the name all the cult's women are required to use when answering the compound's telephone (as stated in the long list of instructions written on the wall next to the telephone). The men are all required to call themselves "Michael" on the phone.