A pope does not have to change his name but most do. It is symbolic of Jesus changing the name of Simon to Peter at the time he named him as leader of his Church and the first pope.
At the time of Pope Valentine, popes did not change their name. He received the name Valentine from his parents.
There have been 12 popes who have taken Pius as their name.
No Pope is obligated to change his name. This is a pious tradition (not Sacred Tradition). The practice arose when a pagan convert to Christianity became Pope and changed his name from Mercury (after the pagan Roman god) to John II in 533 C.E. Until then, the Popes kept their original names, from Peter (#1) to Boniface II (#55). Between John II (#56) and Sergius IV (#142) in 1009 C.E. only a few Popes changed their names. But since Sergius IV, it has been common practice for all Popes to change their name when elected pontiff except Adrian VI and Marcellus II.
Popes do not elect cardinals, they name them.
There have been no popes named Jude.
There have been six popes named Adrian and six popes named Paul.
There have been 12 popes named Pius.
There have been 23 popes named John but none with 21 as a maximum.
the popes live in the papal apartments in the apostic palace in vatican city
There have been 23 popes named John, the most popular name by far.The most popular name historically chosen by the popes is John. No less than 23 popes have taken the papal office under this name.
Benedict is the name used by 15 popes. Pope Benedict X was an antipope and not counted as a legitimate pope.
Both Leo and Innocent have been used by 13 popes.