Hi Tia – as of now, you aren’t able to change the design from public to private. However, this is a feature that is in the works and will be released soon. Once released, admin users will have the option to change designs from public/private.
The user can reload their design on the specific product, but for now they’d have to start from scratch to put it on a different product. Reloading a design on a different product is on our feature roadmap and will be developed and released at some point in the future.