But just like Brexit, any final decision must be ratified by a referendum. The group of islands, located roughly 1,900 miles northeast of New Zealand, were first spotted by Captain Cook in the 1770s, and by the late 19th century was a British protectorate. Since 1975, it has been autonomous, although closely aligned with the Kiwi nation.
The government of the Cook Islands initially created a committee to come up with an indigenous name which would sit alongside its existing one.
But they rapidly deciding to ditch the idea of maintaining any link with the Captain, opting to adopt a standalone name in the Maori language.
Committee chairman Danny Mataroa said: “When the committee members, which include Cook Islands historians and people with deep traditional knowledge, met we decided it was time we change the name of the country.
Mr Mataroa said the new name would have to incorporate the nation’s Christian faith as well as its Maori heritage.
He added: “And it must instil a sense of pride in our people, and unite our people. It must also be easy to say.”
Deputy Prime Minister Mark Brown backed the idea but stressed the final decision would need to involve the Cook Islands’ 12,000 residents.
The committee is considering a list of 60 potential names taken from public submissions, and one will be presented to the government in April.
Avaiki Nui, a popular though not universally accepted name for the islands, is likely to be one of them, although in 1994, a referendum considered the idea of changing the name accordingly was defeated.
Mr Brown told Radio New Zealand: ”I’m quite happy to look at a traditional name for our country which more reflects the true Polynesian nature of our island nation.
“I think the first steps are to find out what the public appetite actually is for a change of name.”
However, opposition leader Tina Browne was less certain, suggesting voters were likely to be evenly split on any proposal put before them.
She said: “Whether or not it’s going to command a support of the majority, it’s very hard to tell.”
Captain Cook first saw Manuae, a southern atoll which forms part of the islands, from The Resolution, the ship which he commanded, in 1773.
The southern group of islands became known as as Hervey Islands, after Augustus Hervey, a Lord of the Admiralty and politician.
The name was changed to Cook Islands in 1824 by Adam Johann von Krusenstern, a Russian explorer and navigator.
Cook Islanders first settled there 1,500 year ago, having arrived from what is now known as French Polynesia in large canoes.