The current pope (October 2015) is Pope Francis who was born Jorge Mario Bergoglio.
From Saint Peter to Pope Francis there have been 266 popes.
There have been 12 popes who have taken Pius as their name.
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.
In most cases it serves to indicate the number of popes who have taken that name. Benedict XVI means that there were 15 popes prior to the present one who have taken the name Benedict. Given the long history of the church and the vagaries of human history (to say nothing of the controversial anti-popes) the numbers are not always accurate. If I am not mistaken, the popes named John have not been accurately counted. There may be others. But there is really no significance beyond that; it's just a way to tell them apart.
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.