No, the Church has had 266 popes (as of 2013) and all have had names.
There have been no popes named Kenneth.
There have been 6 popes named Sixtus.
There have been 13 popes named Leo.
There have been six popes named Adrian and six popes named Paul.
There have been 13 popes named Innocent.
There have been no popes named Jude.
There have been 15 popes named Benedict. Benedict X does not count as he was an antipope.
There have been 16 popes named Gregory. Gregory XVI reigned from 1831 to 1846.
There have been 8 popes called Urban.
Most popes wore name John , but to appropriately answer ur question... These 2 names were used 13 times: InnocentandLeo{| ! style="text-align: left" ||! style="text-align: left" ||}
There have been 6 popes who chose the name of Paul.
There have been 12 popes named Pius.