Possibly a nickname, usually short for Vanessa, yet mostly becomes preferred name. Usually given to a girl with spirit, beauty and individuality.. You don't mess with Venny.
Person A: "Do you want to invite Venny?"
Person B: "Oh you mean Vanessa?"
Person A: "Umm yeh but I just know her as Venny..."
Person A: "She was giving me a dirty!"
Person B: "Nah that's just Venny."