When, in 1410, Baldassare Cossa was elected Pope John XXIII, there was only one small problem, the church already had a pontiff (Pope Gregory XII).
In fact, it had two, as Pedro Martinez de Luna claimed to be Pope Benedict XIII. This was the time of the Western Schism, a spilt within the Roman Catholic Church, which lasted from 1378 until 1417.
Cossa took the name John in honour of Saint John the Baptist, a reliquary of one of whose fingers he possessed. He only remained 'pope' for five years; he was deposed in 1415 and tried for a number of crimes. Baldassare died in Florence in 1419 and is buried in the Baptistery.
Although the Catholic Church regards him as an antipope, the inscription on his tomb (the work of Donatello and Michelozzo) proclaims: 'JOANNES QUONDAM PAPA XXIII'.
When, in 1958, Angelo Roncalli was elected pope, he chose the name John XXIII, thus affirming the anti-papal status of Baldassare Cossa.