The biblical explanation:

The first pope was the apostle Simon, Jesus personally renamed him to Peter, meaning rock, because he was being reborn to become the foundation/rock of the new church. Subsequent popes rename themselves to signify their rebirth.

The historical explanation:

in 533 John II decided it would be inappropriate for a Pope to be named after a pagan god (Mercurius, his birth name), by the 10th century popes were largely from France and Germany but wanted to sound like their italian predecessors and so began renaming themselves. This happened enough to just become a tradition, with the last pope not getting renamed being in 1555 (Marceullus II)