Years ago, when Pope John XXIII died, the topic of the day was who would replace him. On the very short list was Cardinal Sicola, who was absolutely perfect, except for one thing. The College of Cardinals decided the world just wasn't ready for a Pope Sicola.
Of course, the Pope adopts a name of his choosing on taking office, so the cardinal would not have been named Pope Sicola, unless he really wanted to be. The current Pope, John-Paul II, took his name to honor his predecessor, John-Paul I. The next Pope may well decide to take a name to honor John-Paul II, or he may not. Nobody knows.
The one safe bet is he won't choose the name "George-Ringo".