As far as I know, in the U.S. you are free to print your own paper currency, just so long as it doesn't conterfeit that which is produced by the Federal Reserve Bank. Also, there's nothing illegal about conducting transactions with it either, provided you can find willing trade partners.
This is not the case, when a 'private' currency gains traction or seemingly encroaches a territory, which is traditionally assigned to government ─ it gets shutdown.
https://www.nytimes.com/2012/10/25/us/liberty-dollar-creator...
https://www.openpr.com/news/25136/TUC-IMPROVING-THE-US-ECONO...
Or if they had been owned by Disney for that matter...
It's been around for a long time.
Indeed, this is currently done. For example:
The other caveat is that if someone owes you a debt you can't require them to pay in your own "funny money" currency. You have to accept US dollars if offered, otherwise the debt won't be legally enforceable.