Jenny today is used as a pet form of Jennifer, hence ultimately deriving from Gwenhwyfar.
Jenny used to be a nn of Jane (a feminine form of John, of course), and still is, I suppose. But today's Jennys are much more likely to derive from Jennifer.
Though I'm still confused as to why Jessica said John meant "Yahweh", forgetting the "is gracious" part. (No offence Jessica!)