Many dialects in the Appalachian regions are closely related to middle English accents. They haven't changed since the earliest settlers in the "new world." For linguists, the Appalachians are a rich source of evidence and a genuine pleasure to listen to. So I would take the Appalachian comment as a compliment if I were you.
That said, I pronounce
Caroline and
Carolyn differently. I live in the U.S. / Pacific Northwest, if that makes a difference. I have never heard them pronounced the same way. Personally, I prefer the formality of the
Caroline (= line) pronunciation.
In the end, I think there are regional differences in how names / words are pronounced. People in the general population aren't putting in that much thought to a name. We namenerds are the ones who tend to over-think them. :0)