Well possible! So it would be like with the "Germani", whose name was probably coined by the Celts (meaning "neighbour"). So the Fenni may have been the "marsh people" in some Germanic language, as a translation of the name the Finns gave to themselves (when?).
There used to be a German word "Fenne" meaning "swamp", but it's not in use any more. The Grimm dictionary says that there was still "fehn" and "fenne" around in their time (mid 19th cent.), but it has now died out completely.
I don't know much about the history of the Finnish people and what happened to them during the migration of nations. I have always wondered why their language is related to Hungarian and obviously to nothing else.