The correct name for the eighth month of the Hebrew calendar is Marcheshvan. (See here and here.) This is how the name of the month appears throughout the Talmud (to the best of my knowledge) see e.g. Rosh Hashana 7a.
Colloquially, it is often shortened to just Cheshvan (to the extent that many think this is the correct name of the month).
Where is the first place we see the name written as Cheshvan?
Pri Chadash to Even HaEzer 126:7 writing in the latter half of the seventeenth century seems to assume that the "real" name is Cheshvan, so I imagine we would see sources before his time using the name Cheshvan for the month.