None, Benedict XVI is the first.
Pope Benedict XVI is the only pope with the name of Josef Ratzinger.
Popes do not choose a surname when elected to the papacy. Before elected, though, Benedict XVI's name was Joseph Ratzinger.
There has only been one pope by that name - Pope Benedict XVI.
His name as pope is just Benedict XVI. Popes do not have last names when they become pope.
Joseph Alois Ratzinger
The current Pope Benedict XVI was named Joseph Aloisius Ratzinger at birth.
His name was Cardinal Joseph Alois Ratzinger.
Joseph Alois Ratzinger was his original name.
His complete name is Josef Alois Ratzinger.
Joseph Alois Ratzinger was his original name.
Prior to Benedict XVI there were 14 other popes with that name. Pope Benedict X was an antipope and does not count.
The full name of Pope Benedict XVI before he changed it was Joseph Alois Ratzinger.