I was checking out the list of pope names by frequency on Wikipedia in search of minutia to defend my assertion that Pope Francis was the first new Pope name a long time and noticed that there were two popes named Pelagius (I and II) but there's also a Pelagian heresy that predates their pontificate.
So, why Pelagius? Or didn't the Popes think that hard about their names back then?
That's interesting! Catholics tend to avoid using heretical names. In fact, I believe that it's in canon law that baptismal names cannot be the names of heretics, and that it is the priest's duty to prevent such a name from being used. So it is very strange that any pope would the name of a known heretic.
So why do we have two popes with the name of a heretic, and a very recent one, at that? Perhaps it is because Pelagius of the heresy himself might have denied important aspects of that heresy:
This theological theory is named after Pelagius, although he denied, at least at some point in his life, many of the doctrines associated with his name. (Wikipedia)
Still it is strange, because the name would still have been associated with the heresy. So let's look further. From Wikipedia:
Beginning in the sixth century, some popes adopted a new name upon their accession to the papacy; this became customary in the 10th century, and every pope since the 16th century has done so. [...] During the first centuries of the church, the bishops of Rome continued to use their baptismal names after their elections. The custom of choosing a new name began in AD 533 with the election of Mercurius.
It is because "Pelagius" is the original name of both popes! 1
It's still a question exactly why neither chose to follow the example set by Mercurius (named after the Roman god Mercury), but I suppose the practice was only taking root around that time.
1: This is not certain, but seems very probable: the name-changes of other popes around that time are well-recorded but no change is recorded for either of these popes, and I can find no record of either Pelagius being called by a different name before becoming pope.
Perhaps this can help with an answer to your question if I have understood it correctly.
If 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 (566-561) 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.
