sorry, most of what you read on Nameberry is fictional, or muddled Chinese whispers,
Jana (feminine) is Arabic for "Paradise" or "garden", small bird is "uṣfūr" (masculine); the closet Sanskrit is Jina (masculine), meaning "Victor/victorious", or "old", or
Jana "birth, offspring" (also masculine, and therefore also "person, man");
Jena is upper Sorbian (a slavic language of eastern Germany) for "one" when feminine; while Jene is a rather archaic
German feminine/plural pronoun cognate with "yon", which makes me think the town has never had a real name, it was just "that" place.