I have been researching this subject and am confused about why Peter named Linus the next pope while he was still alive. Did Peter just decide he didn’t want to be pope anymore?
We can’t be sure that’s how it went. But he could name his successor without himself resigning. For example, he could say, “when I die, Linus will take my place.”
This is essentially what Popes today do. They basically say, “when I die, the person who receives x amount of votes in the Conclave will succeed me” (or whatever the governing rules say that they promulgate or choose to leave in force from a previous pope).