Very interesting! I didn’t know Paul’s mother was named Mary. Still, the double meaning would have been obvious to him. “Mother Mary” is a term that applies to St. Mary all the world over. It’s much different than saying “My mother, Mary” to refer to one’s own earthly mother. Still, perhaps British english is different in this respect than American English. In America, one would not usually say “Mother Jane” or “Mother Donna” to refer to their own mom. That would be a strange thing to say. As a native English speaker, I know that it is very unusual to refer to your own mom using her first name. At the same time, if someone said “Mother Mary” most people would immediately know who was being referred to.
If this was indeed a song about his own mom, I’m confident he chose the wording purposefully to refer to his mother, and at the same time invoke the thought of the universal mother that most people can relate to, the Blessed Mother Mary.