The form of the name on the ossuary in question is Mariamenou. This is a Greek genitive case, used to indicate that the ossuary belongs to Mary (it means 'Mary's' or 'belonging to Mary'). The nominative would be Mariamenon. Mariamenon is a diminutive form, used as a form of endearment. The neuter gender is normal in diminutives used for women.Please read it all if you have not already done so, but I wish to comment briefly on a couple of points. First, the name "Mariamne" is also found in Hippolytus' Refutatio where he is describing the teachings of the Naassenes, whom, he says, "ascribe their system, through Mariamne, to James the Lord's brother" (Haer. 5.7). Hippolytus is writing in the early third century and discussing the Naassenes in the ?mid second century.
This diminutive, Mariamenon, would seem to have been formed from the name Mariamene, a name which is attested twice elsewhere (in the Babatha archive and in the Jewish catacombs at Beth She’arim). It is an unusual variant of Mariame. In the Babatha document it is spelt with a long e in the penultimate syllable, but in the Bet She’arim inscription the penultimate syllable has a short e. This latter form could readily be contracted to the form Mariamne, which is found, uniquely, in the Acts of Philip.
So we have, on the one hand, a woman known by the diminutive Mariamenon, in the ossuary, and, on the other hand, Mary Magdalen, who is always called in the Greek of the New Testament Maria but seems to be called in a much later source Mariamne. Going by the names alone they could be the same woman, but the argument for this is tenuous.
But this also raises the question of whether it is correct to identify this early Christian figure, Mariamne, unequivocally with Mary Magdalene, as the film-makers do. We do not know who Mariamne is in the Naassenes discussed by Hippolytus. On Apocryphicity, Tony Chartrand-Burke asked whether Mariamne of the Acts of Philip is indeed Mary Magdalene, raising the possibility that she is Mary of Bethany. I've done a little reading since then and it seems that scholars are divided on the issue of the identity of this character in the Acts of Philip. It is clear that she is Philip's sister, but it also seems that she shares traits commonly associated with Mary, Jesus' mother, and Mary of Bethany, as well as Mary Magdalene. Stephen Shoemaker, for example, argues in a couple of publications that "the Gnostic Mary" is a kind of composite Gnostic character with characteristics from these several Marys. I will add some bibliography tomorrow for those who are interested.
The import of this is to detract still further from the claims that this particular cluster of names is remarkable. For Jacobovici, it was the turning point for him to discover that Mariamne was Mary Magdalene's "real name". The bad news for him is that it is only her real name if one goes with a fourth century text, the Acts of Philip, that has no chance of containing first century traditions, and which itself is not explicitly talking about the Mary Magdalene we have mentioned in the Gospels. Wherever she appears in first century Christian texts, she is always "Maria", as are the other several Marys in the New Testament. Mariamne is not, I am afraid, the hoped for "Ringo".