Mary said, "All popes are considered to be "Peter" by Catholics.  When a pope dies or resigns, they often comment that they are waiting for the "Next Peter in the line"

That really isn't true at all.  Peter is considered the first pope, but no one is considered to be able to take Peter's place, which is why no pope has ever used the name.  No one in the Catholic Church calls the pope "Peter" or uses "Peter" as a generic name for the pope.  It just isn't done.

The point of Malachy's prophecies was to say something about each pope that sets him apart from all other popes.  Descriptions like "De medietate lunæ" (from half the moon), De labore ſolis (laborer of the sun), etc., all describe each pope in a way that intends to identify him as unique and different from all other popes.  To have the name "Peter" would indeed make him different from all other popes since no pope has chosen to take that name and probably won't have that name unless he is born with it.  Lots of popes have been from Rome, but if the NEXT pope were from Rome after the last 3 were from different parts of the world, that would be something significant.  At one point, you became pope by becoming the bishop of Rome.  Today, a cardinal becomes bishop of Rome by becoming Pope.  So all popes are connected to Rome in some fashion, however, the context of Malachy's writings are that being "PETRUS" and being "ROMANUS" help identify him in some fashion. 

Overall, it should not be difficult for us to face the reality of the fact that Malachy simply cannot be relied on as a source here.  Francis may or may not be the last pope, but I'm not going to base on judgment on whether he is by what Malachy said.

Shalom, Joe