Copyright. There is copyright upon creation, so creative people have copyright without doing anything in particular except creating their own work. But to sue in federal court, the work must be registered. $65 per registration for the visual arts (U.S. copyright office), and pretty much irrefutable proof that the work was created before the registration date. This mostly protects against 1 to 1 copying of the original work, so, it's not very strong, and particluary not strong if there isn't much creative expression in the work.
Trademark. To protect the good will developing around a brand, however, register with the Trademark office. These go through some scrutiny, but trademarks last forever so long as they are used. Trademark law protects the name or mark (or a confusingly similar name or mark) from being used by competitors. Like, for example, 'fruit bat pottery' and 'vampire bat pottery.'
Design Patents. Finally, for decorative design that is both original, and valuable enough to go through the trouble, there is the design patent with the Patent Office. Patents have a well deserved reputation for being difficult to get. However, there should be functional pots that would qualify for this, so don't dismiss this as impossible. The Captain Picard tea set comes to my mind as the kind of thing a design patent will protect. And a design patent holds out the possibility that it would prevent a greater variety of copying of the ideas in work than copyright protection.
I am not giving legal advice people - don't ask me for any. go get your own attorney.