The names being considered so far reflect Christianity, Maori heritage and national pride.
"It must also be easy to say," Danny Mataroa, who heads the name change committee, said.
Previous attempts to change the name of Cook Islands — a self-governing territory with political links to New Zealand — have been unsuccessful.
Citizens voted to keep the name, taken after James Cook who first arrived there in 1773, in a national referendum in 1999.
But Mr Mataroa said while previous attempts to change the name mainly involved the main island of Rarotonga, where 75 per cent of the population lived, this time it involved traditional leaders from all 12 inhabited islands.
"This is the first time we've actually gone this far," Mr Mataroa said.
Cook Islands have a long history with name changes.
Historians believe Cook Islands were first inhabited by Polynesians from Tahiti in the 6th century.
Spanish sailor Alvaro de Menda a de Neira sighted the islands in 1595 and named them "San Bernardo" or Saint Bernard.
Then in 1606, the first European to step foot on the islands, Portuguese navigator Pedro Fernandes de Queiros, renamed the region "Gente Hermosa" or Beautiful People.
Captain Cook visited in 1773 and 1777 and renamed the islands "Hervey Islands". "Cook Islands" became the current name around the 1820s.
Cook Islands became a British protectorate in 1888 and was included within the boundaries of New Zealand in 1901 until 1965 when it was granted autonomy by Wellington.
Cook Islands is a popular South Pacific destination due to its stunning turquoise lagoons, spectacular reefs and tropical rainforests and lush mountains.
A popular activity for tourists is visiting the Rimarau Burial Caves, which according to legend, house the skulls and bones of warriors killed in battle.