The month of Cheshvan is called by many MarCheshvan. Are both correct or which one is more correct?
I don't know that I'd put money on this one, but I heard that the original name was warach-sheman (an aramaic version of yerech shmini) and that the dialect allowed for an interchange between the w (our vav) and the m sound, corrupting it further to marach-shewan.
After a search, I found a "What's the truth about..." on this subject which also talks more to the point of the question.
The actual name is Marcheshvan - it is derived from the Babylonian, as are all of the names of our Hebrew months (note that the current names on the Hebrew months only appear in Tanach in books that occur during or after the Babylonian exile). I do not recall the exact Babylonian version of it, but a simple Google search can turn up that info. All of the cute derashot about mar meaning drop or bitter are post-facto ideas that, frankly, I am not sure where they came from.
MarCheshvan simply means
bitter Cheshvan -- bitter because the month has no holidays in it. Both are correct, but MarCheshvan is used when announcing the new month.