Now beyond the obvious - such as the fact that you can’t select the name and monicker of a real Pope in the past, are there any specific regulations on the naming system?
Are there any names a Pope can’t choose?
Although a pope is free to choose any papal of his desire, there would seem logic that any name chosen by a pope should not not be foreign to the Catholic Faith.
The basic rules for choosing a baptismal name would seem to apply here.
Canon Law states that names foreign to Christianity are not to be given to infants.
Can. 855 Parents, sponsors, and the pastor are to take care that a name foreign to Christian sensibility is not given.
Foreign names here simply means offensive to the Catholic Church, the dignity of the child and Christianity in general.
I guess Lucifer would be out of the question!
Pope John II (532-535) was the first pope to change his name, it was due to the fact that his given name Mercury was that of a pagan Roman god and thus he was trying to avoid a scandal.
The pope Pelagius I (556-561) and Pope Pelagius II (579-590), on the other hand, both kept their given names which did not seem to either Pontiff to be a source of scandal considering the fact that the Church had just went through the Pelagian Heresy a century before! This heresy is named after its original heretic Pelagius (c.360-418).
Another way of looking at this is ask ourselves a rather simple question. For example: Should a pope change his given name if it were Apollinaris in light of the Apollinarism Heresy?
Yet the Church has both a St. Apollinaris (1st or 2nd Century) who predates Apollinarism and a St. Pelagius (912-984), who postdates Pelagianism.
There seems to be a distinction between the names of pagan gods and those of heretics. A close look at a list of Christian heresies shows us that several of the instigators of certain heresies had Christian names in one form or another. Even the names of Anti-Popes have not deterred the popes from using a particular papal name.
According to the Catholic Answers article What are the criteria for a pope in choosing his new name?:
There are no official criteria, but a pope usually chooses to honor a predecessor or someone he admires.
As for restrictions, there are none, but
it is an unwritten custom that popes do not choose the name Peter. It is generally considered a matter of prudential judgment for popes not to invite comparisons between themselves and the pope Christ himself chose.
For more background, please see a parish article How do Popes Choose Their Names?
There is no canon law requiring that someone take a different name upon becoming pope, although it has become tradition since Pope John II (died 535) who chose John because his name was Mercurius (after the Roman God Mercury).
Reasons behind the names have varied: more Italian sounding names (Pope Gregory V), honoring the Second Vatican Council (Pope John Paul I and Pope John Paul II), appealing to Saint for protection and to signify peacemaker (Pope Benedict XVI), to honor a saint (Pope Francis), etc.