One issue with a EU-US trade deal was that US farmers didn't want to have labelling rules to inform the consumer. Indeed they specifically wanted to remove the option that I, the consumer, had in deciding what to eat. The US government negotiating objectives call for ‘new and enforceable rules to eliminate unjustified trade restrictions or unjustified commercial requirements (including unjustified labeling) that affect new technologies.’
As swindling the consumer the is the M.O. of big business. I'd rather err on the side of the consumer. Naming protections - be it country or region of origin or trademarks in general - do not restrict consumer choice. I can buy "greek style" cheese if I want "feta style" that's not made in Greece.