Milne said Stolen Rum quickly removed reference to the Smoke and Coke name.
The drink is now referred to by the less memorable name Smoke and Cola.
"You will never see the word 'coke' written with any [alcohol brands]," Milne said.
"But if punters go into a bar and order a Smoke and Coke, we hope it takes off."
Coca-Cola NZ spokesman Andrew Hewett said his company was duty-bound to ensure the brand was not misused.
"As the Coca-Cola marks are registered ... they are incontestable and the value of that incontestability for the Coca-Cola Company should not be underestimated."
Trademark and litigation lawyer Gus Hazel, a partner at James & Wells Intellectual Property, said emerging brands often tried to piggyback off more established ones - and were usually stomped on swiftly. "Coca-Cola is very aggressive in how it protects its brands, its trademarks. You can appreciate why as so much of its business rides on its brand.
"Over time a brand can become diluted and lose value if too many 'low level' infringements are left unchallenged."
Hazel said Coca-Cola had registered its trademarks in relation to almost "everything you can think of" - not only drinks, but also such seemingly unrelated products as mirrors and sleeping bags.
It had recently become embroiled in trademark stoushes with Pepsi-Cola over the shape of bottles.
New Zealand companies have been involved in other David and Goliath trademark battles and come out on top.
Last year, a Hamilton company won a trademark dispute with tech giants and iPhone maker Apple over registering its product, driphone, at the New Zealand Intellectual Property Office.
The company makes waterproof cases for smartphones and argued its product did not breach copyright of the ubiquitous iPhones.
