I am reading a book (Catholic publisher) which suggests that Mary, the sister of Lazarus and Martha, is also the Mary called Magdalene, and is the same Mary who anointed Jesus with expensive oils and her tears while he reclined at table. I am confused by this as I thought they were all different persons. And while we are on the subject, who was Mary of Clopas mentioned as standing by the cross of Jesus? (Jn 19)
The suggestion was just that: a suggestion. There has never been a definitive statement identifying the woman who washed Jesus' feet with her tears and Mary of Bethany (the sister of Martha and Lazarus of Bethany) as Mary Magdalene (of Magdala). Some choose to identify them as the same people, others prefer to keep them separate. I believe the Eastern Orthodox distinguish Mary Magdalene from both women, as does the Church (as they have never officially released a dogma stating these women were one and the same), but someone else may know better than I. However, of course, there is certain people who hold the belief they are all the same.
Mary of Clopas (or Cleopas) is the wife of Clopas (or Cleopas), one of the many Marys that are mentioned in the Gospels. In 1982, Stephen Smalley said that it was "very probable" Mary of Clopas was the mother of James son of Alphaeus (James the Less, often confused with James the Great, and may be the same person as James the Just, who was said to the be the 'brother' of Jesus), given that Alphaeus/Clopas/Cleopas may be the Greek variation of the Aramaic name 'Hilfai'. Some people considered her to be Our Lady's sister, given her name is mentioned after the phrase 'His mother's sister' in The Bible, but this, too, has never been defined, and some consider her to be Our Lady's cousin (as Hebrew/Aramaic had no word for 'cousin' and for the simple question: why would parents name both daughters the same name?) or sister-in-law (being the sister of Joseph).
I hope I helped answer your question; I am sure there are others more knowledgeable than I and may answer this question better.
Studies of first -century ossuaries suggest that about 25% of the Jewish women were named Mary. Depending on your reading of the verse, there may be as few as two women named Mary at Jesus' crucifixion or as many as four. There was a conflation of Mary Magdalene, the unnamed woman who washed Jesus' feet at the house of the Pharisee, and Mary, the sister of Martha and Lazarus in a homily delivered by Pope Gregory the Great. Ever since then Mary Magdalene has been shown in Christian art as a prostitute, usually dressed in red with her head (and a lot of bosom) uncovered, bearing a bottle of perfume. and having a skull close by. There is nothing in the Gospels to indicate that this was the case.
Mary Magdalene would have been a woman of some means, to have underwritten the expenses of Jesus and the disciples. She would have had to have been ultra-rich to have afforded houses both in Magdala, on the shore of the sea of Galilee and a house in Bethany. If she earned this money through prostitution, we would then have the circumstance of Jesus and the disciples living on the proceeds of prostitution. I don't know about you, but that idea is just anathema to me.