St. Malachy wrote a list of Popes, giving each a prophetic saying, to indicate what his reign would be like. So when St. Malachy called the next Pope, “Peter the Roman”, he was not indicating that this Pope would take the name “Pope Peter”, nor that the personal name of the Pope would be “Peter”. Instead, the phrase indicates what that Pope’s pontificate will be like. His reign will emphasize the authority of Peter and his successors, and the primacy
of the Roman Catholic Faith: hence the name “Peter the Roman”.

— Ronald L. Conte Jr.