Apologies if there is not a good answer to this but I was wondering how papal names are chosen. Is there a specific tendency for taking a papal name that is associated with a tradition or strain of thought? For instance does the name Benedict imply that you are from a particular subset of orders, does Pius imply that you have a particularly high Christology? Or are the names essentially down to the Pope in question's relatively arbitrary choice? This question could I suppose be reframed as do Papal names carry any particular connotations?
For example, Benedict XVI chose his name after St. Benedict and Pope Benedict XIV.
Pope Pius XII likely chose "Pius" because he is in the episcopal lineage of Pope St. Pius X.
John Paul I and II chose theirs after the preceding John XXIII and Paul VI.
Christ chose St. Peter's for him. ☺
Other than that, yes, "the names essentially [come] down to the Pope in question's relatively arbitrary choice". After they are elected, a cardinal asks them which name they choose.
William Portier, chair of Catholic theology at the University of Dayton, expounded upon how popes choose their papal name in an interview with CTV News.
First off, Catholics recognize Jesus renaming Simon to Peter as the first example popes taking on a different name.
"In the Bible, when you get a new job from God, you pick a new name or you're given a new name, and that's the idea -- they feel they've been chosen to do this very weighty job and they need a name that will sort of help them and inspire them," Portier said. “It’s also a signal to the rest of the church and the world.”
Despite that, early popes just used their given names. It wasn't until Mercurius in 533 (who felt that a name based on a Roman god was inappropriate for the head of the Christian church, and chose instead the name John II) that the tradition began of each pope picking a different name.
Portier identifies several different reasons for popes picking their names (the pope decides whichever reason they feel is most important to them).
To show continuity with the previous pope by picking the same name
Pope John Paul II -- Benedict XVI’s predecessor -- chose his name to honour his predecessor, Pope John Paul I, who died just one month into his reign. By assuming his name, John Paul II signalled his intention to continue the previous pope's work during his papacy.
To honor and affirm the work of previous popes
Pope John Paul I had also paid tribute to previous popes. His moniker was a composite of the names of two previous popes, John and Paul, who had guided the church through the tumultuous Second Vatican Council (known as Vatican II) in the 1960s. Many consider it to be one of the most important -- and controversial -- periods in the church's history, as leaders attempted to modernize relations between the church and the secular world.
"(Pope John Paul I) wanted to show he was not going to deviate from their path and would be faithful to what they had done," Portier said.
To express a desire to emulate the work of a previous pope or other exemplary person of faith
Pope Benedict XVI, whose decision to step down from the papacy for health reasons spurred the latest conclave, also chose a name that reflected previous church leaders whom he hoped to emulate.
One was Pope Benedict XV, who reigned during the First World War and served as a voice for peace; the other was a 5th century monk who sought solitude in the country and worked to spread the Gospel around Europe. Though he wasn’t a pope, he set an example that Benedict XVI hoped to follow.
At the time of the article's writing, "Pius" was considered a possible name for the 266th Pope (who became Pope Francis) as a reference to Pope Pius XI who fought for the papacy's independence from secular states and continuing church tradition. Portier noted that this would be a surprising and "scary" choice should a Latino or North American pope, a non-traditional choice, be elected.
To deny the legitimacy of an imposter pope by picking the exact same name and number
Pope John XXIII, for example, managed to erase a purported papal imposter from the history books with his name choice.
During the Great Western Schism of the 1400s, three men had claimed to be pope at the same time, including one who took the name John XXIII. He was later declared an imposter or “antipope” and deposed, but historians and scholars have often debated whether he actually had a legitimate claim.
By choosing the name John XXIII when he became pope in 1958 -- which he said was in honour of his father and other previous popes who started their reign later in life, like him -- the 77-year-old pope effectively relegated the deposed papal claimant to a footnote.
“By taking that name, he erased the other pope from history, and he was a historian so he knew that,” Portier said.
To express a sense of unity with other popes from the same geographic region
If the Cardinals were to choose an African pope, he could choose to assume the name of one of several previous popes who had connections to North Africa. Pope Victor I, who reigned during the 14th century, hailed from North Africa, while Pope Miltiades and Pope Gelasius I were from Rome but are believed to be born to families of African origin.
To honor a saint known for a cause they would like to focus on
The interview with Portier was written before Jorge Mario Bergoglio chose to be named Francis, but fortunately that pope publicly shared his reasons for picking a unique name (emphasis mine).
Some people wanted to know why the Bishop of Rome wished to be called Francis. Some thought of Francis Xavier, Francis De Sales, and also Francis of Assisi. I will tell you the story. During the election, I was seated next to the Archbishop Emeritus of São Paolo and Prefect Emeritus of the Congregation for the Clergy, Cardinal Claudio Hummes: a good friend, a good friend! When things were looking dangerous, he encouraged me. And when the votes reached two thirds, there was the usual applause, because the Pope had been elected. And he gave me a hug and a kiss, and said: “Don’t forget the poor!” And those words came to me: the poor, the poor. Then, right away, thinking of the poor, I thought of Francis of Assisi. Then I thought of all the wars, as the votes were still being counted, till the end. Francis is also the man of peace. That is how the name came into my heart: Francis of Assisi. For me, he is the man of poverty, the man of peace, the man who loves and protects creation; these days we do not have a very good relationship with creation, do we? He is the man who gives us this spirit of peace, the poor man … How I would like a Church which is poor and for the poor!
Francis also shared that his colleagues jokingly suggested he should have chosen the name Hadrian, because Hadrian VI was a reformer and they felt the church needed reform, or Clement XV to get back at Clement XIV for suppressing the Jesuits (of which Pope Francis is a member).
The first Pope to choose a papal name was John II, who felt his own name Mercurius was unsuited to papacy, being that of a Pagan god, and chose to honour his martyred predecessor instead. The last Pope to retain his Baptismal name for his Pontificate was Marcellus II, though this was extremely unusual then.
There are no canons or regulations which constrain the choice of name for a Pontiff. Any name at all will do, though usually the same few names are picked again and again — a little under half (129) of all 264 popes have used the same ten names: John, Gregory, Benedict, Clement, Innocent, Leo, Pius, Stephen, Boniface and Urban.