What to do about brands…

Hey all, so the company I work for has a UK exclusivity agreement with a supplier. We have just started trading on Amazon and the suppliers brand is not registered. For speed we didn’t worry about it and just listed some under our own brand ( as we have personal GS1 codes) but now we are starting to hit roadblocks where a seller in the US is listing the same products in the same way meaning that unless we get custom codes for everything we would be listing offers against the other sellers brand for the UK. Personally I think it’s worth getting permission to register the brand properly on Amazon but what does everyone else think? Also has anyone had experience with registering a brand on behalf of a supplier?