Philip Kosloski of Aleteia poses this question. He gives a very weak answer leaving the question in doubt, although he does provide the correct answer when he cites the Catholic Encyclopedia and Saint Jerome. I tried to enter a comment but I need to have a password which I don’t have. Rather than dropping the question, I thought it should be answered briefly for our readers. That answer is as follows:
Yes, Mr. Kosloski, Mary of Cleophas is the same as the mother of James the Less, Jude, Simon, and Joses and Salome. Of course she was not born to Saint Anne and Joachim, or else they would have given her some other name than Mary. How could they give the same name to two daughters? The tradition has been from the earliest centuries that Anne and Joachim had only one child, Our Lady Mary. In the womb of Saint Anne, in her house of Nazareth, was achieved the Immaculate Conception. It would have been unbefitting after that unique event of grace for any other conception to have taken place in so holy a place as hosted the Immaculate Conception. Furthermore, this Mary of Cleophas was old. Assuming she was the mother of James the Less. James was the brother of Salome who was the mother of the “Sons of Thunder,” James the Greater and John. Therefore, she had to be advanced in years. Jerome was acquainted with the tradition of the early Church which must have handed it on that Cleophas and Alpheus were the same person, one name being Greek (Cleophas) the other Hebrew (Alpheus). And the tradition was that this man was the brother of Saint Joseph as you mention in your article. This is also why Saint Paul calls Saint James the Apostle “the brother of the Lord” (Galatians 1:19). The relation being not of blood, but because he was the son of Alpheus, the brother of Saint Joseph.