Cyprus this year applied to the European Commission to have the name haloumi protected.
In the EU-Canada free trade deal settled last year, Canadian exports of feta, asiago, gorgonzola, fontina and munster will have to stipulate it is "in the style of," and won't be able to have Greek flags or references that might suggest it is made in Greece.
Wellington cheesemaker Michael Matsis of Zany Zeus specialises in haloumi cheese and also makes feta.
He has kept up with the big feta debate and believes the most important thing is maintaining a quality product ensuring consumers know what they are buying.
He said in Cyprus haloumi is made with a combination of sheep and goat milk and mint folded into it.
"If we made a haloumi like the Cypriots then the product would have no acceptance here, so we've developed a product that we have developed for the New Zealand palate that is less salty, less firm and has good grilling characteristics.
"The same with feta," said Mr Matsis, of Greek Cypriot descent.
"We try to make a feta that is not just a dry, chalky, flavourless product. We are trying to make one that is full of flavour and has a nice balance of moisture and creaminess.
"But I believe if the quality is there, we should have the ability to call it feta cheese."
Fonterra, the owners of the Kapiti and Galaxy brands of cheeses, among others, were not available for comment.
Auckland lawyer John Barker, who specialises in IP in food and beverage, said the European Union had had a food protection system since about 1992.