I can easily see how it could be short for
Charlotte, as some derivatives are rhyming versions of other ones;
Polly from
Molly, for example. Cotty could easily be a rhyming derivative of Lottie/Lotty. I suspect that's how
Totty, a vintage derivative of
Charlotte, also came about.
Cotty is slightly better than
Totty, but I wouldn't choose to go by it!
~Charley~
https://www.behindthename.com/pnl/184785