How is the name of a new pope chosen?

Once elected by the 124-strong College of Cardinals in the Vatican, the pontiff chooses what name he will use.
The tradition started in 533, when the pope Mercurious chose to be called John instead of his pagan name. This practice soon gained widespread acceptance.
Another first occurred in 1978, when Albino Luciani chose a combined name, that of John Paul I, to highlight the heritage of the two popes who had reigned before him, John XXIII and Paul VI. In his turn, Karol Wojtyla, chose to take on "the same names chosen by his much beloved predeccessor."