Why would popes choose the name Pelagius in light of the Pelagian heresy?

I was checking out the list of [pope names by frequency](http://en.wikipedia.org/wiki/Papal_name) on Wikipedia in search of minutia to defend my assertion that Pope Francis was the [first new Pope name a long time](http://christianity.blogoverflow.com/2013/03/14/5678-pope-francis-starts-with-a-clean-slate/?cb=1) and noticed that there were two popes named Pelagius ([I](http://en.wikipedia.org/wiki/Pope_Pelagius_I) and [II](http://en.wikipedia.org/wiki/Pope_Pelagius_II)) but there's also a [Pelagian heresy](http://en.wikipedia.org/wiki/Pelagian_heresy) that predates their pontificate. So, why Pelagius? Or didn't the Popes think that hard about their names back then?