Variant form of Fenje. Also compare Fenna. You might also want to take a look at the other entry for Fenja, which is a name from Norse mythology (but has a completely different etymology) that could also have been the inspiration for the parents of some of the modern-day bearers of the name.
Derived from Old Norse fen meaning "moor, marsh, swamp". Also compare Fenrir, which is etymologically related.This was the name of one of two giantess sisters from the Old Norse poem "Grottasöngr", whose tale is considered to be part of Norse mythology.