Hello all!
Just stumbled across this fascinating thread. I wish I could definitively tell you that Margaret converts to Bridget, though I haven't seen that.
There is a book of roughly 30 pages called A Rose By Any Other Name by Judith Wight Eccles that discusses some of the more regular conversion possibilities.
In my own family my Grandmom had a brother named Denis who was called Bob. In the course of researching the townland (southwest Cork) I discovered another family with a Denis (in the 1901 census) called Bob (in the 1911 census). When I told my 87 year old aunt about it over the phone, I asked "sound familiar?" and she agreed. Turns out the wife in that family was Grandmom's dad's sister.
In Grandmom's dad's family there may have been a Jeremiah called William, but I haven't conclusively linked the two names yet. That is a bit of a stretch.
I am starting to wonder if some sloppy or cursively written Latin forms in a baptismal record could have been responsible for the switch. I can tell you from my experience transcribing tithe applotments that Bartholomew can be mistaken for Patrick; Denis for Daniel; Alexander for Aloysius, Mortimer for Murtagh, etc. Many factors come into play, is the name abbreviated, is the initial letter well-formed, partly faded, and so forth. I haven't compared Bridget and Margaret in the baptismal registers, but I can see they both have "r" then a "get" . Margaret is often shortened to Margt which can also look like Mary, depending on who wrote it. You would think the "d" in Bridget would stand out but I've seen them practically disappear in the middle of a word, such as "Cadogan."