The connection between Mary Magdalene and the "Mariamene" of the ossuary is crucial to Jacobovici's story. The name inscribed on the ossuary is "Mariamene e Mara," which means "Mary, known as--" and here there are two possibilities for the word "Mara." According to the Discovery Channel's Tomb Website, "Mara" is a nickname for "Mary," or it could be translated as "master." They choose to translate it as "master," though "Mary, known as (Mary nickname)" seems to me to be a perfectly likely choice.
The breakthrough came for Jacobovici when he was finally able to connect the name "Mariamene" with Mary of Magdalene. He did this through a fourth century text, Acts of Philip, which contains a Mariamne (though not a Mariamene--I'm not sure how much of a difference that makes) whom he claims is Mary Magdalene.
The text he quotes to show this in The Jesus Family Tomb does refer to a Mary, but there is no "of Magdalene" mentioned. I began to suspect that their very identification of this woman in the Acts of Philip with Mary of Magdalene was itself a speculation. So I did a little checking online and came up with this (from Magdalene.org):
The text itself [in the Acts of Philip] describes the adventures of a group of missionaries sent by Jesus to preach his message: Philip, Bartholomew, Philip's followers, and his sister, a woman named Mariamne. Although this woman is never identified beyond her first name, Bovon believes that, consistent with other contemporary references to Jesus' foremost follower, this Mariamne could have been Mary Magdalene.
In other words, the Mariamne of the Acts of Philip could have been Mary Magdalene (if Bovon is correct), and therefore, the Mariamene of the tomb could have been the Mariamne of the text who could have been Mary Magdalene. This is even shakier than it appeared at first.
I also found this observation on CADRE Comments in response to the Tomb website's claim that "Professor Franois Bovon (Harvard University) has determined [from the Acts of Philip] that Magdalene's real name was 'Mariamne'":
First, I should point out that the claim on the website is overstated. Dr. Bovon hasn't "determined" that the woman named "Mariamne" [in the Acts of Philip] is Mary Magdalene…But, as other sources seem to show, Dr. Bovon isn't making a claim of final determination. Rather, he simply "believes" it to be Mary Magdalene (of course, it is an informed belief, but it remains his belief and I have found nowhere that other scholars are largely in agreement with that belief). Certainly, it is an overstatement to claim (as the Jesus Tomb website does here) that "Mary Magdalene is often identified by the name 'Mariamne'" (emphasis added).
The truth is that Jacobovici has to make a lot of leaps to reach the conclusion he's after, and each of those shaky leaps makes that conclusion less likely.