What’s in a name?

For the first few hundred years, new popes kept their baptismal names. That changed in 533 AD with the election of Mercurius. It simply would not do to have a pope named for Mercury, the Roman god (or a Ford product). He said, “Call me John II,” or something like that.
Changing the papal name became the general custom at the end of the 10th century (the 900s), but some popes used their baptismal name even up until the 16th century. The last one was Pope Marcellus II, in 1555.
New popes have taken names in honor of a saint or a previous pope. In the case of the latter, the reason is usually to send a signal that there is some quality or virtue in the previous pope that the new pope wants to emulate. Pope John Paul I named himself for Pope John XXIII who launched the Second Vatican Council, and Pope Paul VI who finished and carried it through. Pope John Paul II named himself for the short-lived Pope John Paul I.
Here are the top papal names: John, 23; Benedict, 16; Gregory, 16; Clement, 14; Innocent, 13; Leo, 13, Pius, 12 and Stephen, 10.