I think the name John Paul is just one name, and the next John Paul will be John Paul III, and the next John will be John XXIV. Otherwise Pope John Paul II would have called himself John XXIV, but he didn’t. Double first names are common, and people who have them don’t use only the first name, they use both as their name, such as Mary Ann, a common name. I also know a guy named John Paul, and he doesn’t answer to the name John at all.