In fact, almost any of those names in Oz that have an 'ar' or an 'er' in them often seem to be shortened to one of the Z forms. I've heard of all of these. There was a Gerry and a Gary in my family, and they were shortened to Gez and Gaz.

Gary - Gaz or Gazza
Barry - Baz or Bazza
Mary - Maz or Mazza
Gerry - Gez or Gezza
Karen - Kaz or Kazza
Carol - Caz or Cazza

As far as Sharon is concerned, I know it's not quite the same, but there was "My Sharona". Only an extra a :-)

My name, Jennifer or Jenny must be one of the most used names in songs actually. As well as the ones mentioned so far - Poor Jenny, Jennifer Juniper and Jennifer Eccles, there was one called "Jenny Jenny Jenny". by Little Richard. My first boyfriend used to sing it to me -

    Jenny, Jenny, Jenny
    Won't you come along with me
    Jenny, Jenny, Jenny
    Won't you come along with me
    You know that I love you
    We could live so happily

    Jenny, Jenny, Jenny
    spinnin' like a spinnin' top
    Jenny, Jenny, Jenny
    Spinnin' like you ain't gonna stop
    The greatest little momma
    You oughta see her reel and rock

    Jenny, Jenny, Jenny
    Won't you come along with me
    Jenny, Jenny, Jenny
    Won't you come along with me
    You know that I love you
    We could live so happily

    Jenny, Jenny, Jenny
    Girl I need you by my side
    Jenny, Jenny, Jenny
    You know I need you by my side
    You know I need you pretty baby
    Your ways I gotta really abide now

    Jenny, Jenny, Jenny
    Won't you come along with me
    Jenny, Jenny, Jenny
    Won't you come along with me
    You know that I love you
    We could live so happily

Then there's that "darlin' sportin' Jenny" in "Whiskey in the Jar".