Since the 6th century the men elected pope have customarily chosen new names — stage names if you will — for themselves. The most popular of these has been John, of which there have been 21. However, the last pope named John officially took the name John XXIII. How can that be?
For all intents and purposes, there was no legitimate Pope John XVI, who, during his papacy was excommunicated during a dispute over who the rightful pontiff was, which was Gregory V. John XVI is actually considered an "antipope" — someone who claimed to be the legitimate head of the Catholic Church, but is not officially recognized as such.
There was also no Pope John XX because of a numbering error.
The second most popular papal name of all is is Gregory, which goes to XVI, followed by Benedict, which also goes to XVI, but again, due to an antipope taking the name (Benedict X), there have technically only been 15 popes named Benedict.
Anyway, as the Economist notes below, the betting odds favor the name 'Leo.' That would be the 14th Pope Leo, and the first since 1903.
Unfortunately there are no odds listed for a Pope Zosimus II.