The move has reignited a long-standing call for an indigenous name for the country, after a vote two decades ago saw voters keep the Cook Islands, named after British explorer James Cook.
The committee, convened in January by a paramount chief, Pa Marie Ariki, is deliberating on a name in Cook Islands Maori, which is similar to New Zealand's indigenous Maori language.
The Cook Islands deputy prime minister, Mark Brown, said the body had a long way to go but had his support.
"I'm quite happy to look at a traditional name for our country which more reflects the true Polynesian nature of our island nation," he said.
The committee, which is already looking at nearly 60 possible new names from public submissions, hopes to whittle the list down to one by April, which will then be passed on to the government for further action.
Previous name change efforts in the Cook Islands fell short, including a national referendum in the mid-1990s, when a majority of Cook Islanders voted to keep the country's name.
"This is the first time we've actually gone this far," said the committee's chair, Danny Mataroa.
He said the previous referendum failed because it was based on deliberations from the main island of Rarotonga, where 75 per cent of the country's population reside.
Mataroa said this time traditional leaders from all 12 of the country's inhabited islands were involved in the process.
He said names being considered by the committee had to incorporate a number of elements important to Cook Islanders, including Christianity, Maori heritage and national pride.
"It must also must be easy to say."
Cook Islanders commemorate the 125th anniversary of women's suffrage at Parliament.
The committee is also seeking to avoid a referendum if possible, because of the costs involved.
However, Brown said a referendum would probably be required if it were to reach that stage.
"I've already said to them that I think the first steps are to find out what the public appetite actually is for a change of name," he said.
The opposition Cook Islands Democratic Party has also lent cautious support to a name change, warning voters are split on the issue.
"Whether or not it's going to command a support of the majority, it's very hard to tell," said party leader Tina Browne.
Mataroa said part of the committee's job was to market the idea to the public, which would hinge on getting the right name.
- Radio New Zealand