Another thing that's weird about it is I can't think of many names it would be a nickname for. Like, with Lauren, you'd probably not emphasize the "Ren" part. So it doesn't seem like a meaty part of a name to riff off of and turn into a spunky little nickname. It's like undercooked toast: not toast, not bread, not really workable. I think this perspective would change if I knew a Renny.
I like Joy, and think it goes well.