Davis, of the Ōrākei Local Board, citing a local historian and reports on a 1940s plan for a flying-boat passenger terminal at the bay, said she was Eliza, Lady Grey, wife of Governor Sir George Grey.
"... hence 'Lady's Bay', which spelling is recorded in a local history and most often in newspapers in the late 1800s, even up to the 1940s," Davis said in papers for this Thursday's board meeting where he hopes to persuade colleagues to support his move.
"Sometimes, but not often, the plural spelling 'Ladies' - with an apostrophe - was written."
He told the Herald that work being done, following subsidence, to build new steps down to the bay gave an opportunity to replace the current sign with one that said "Ladies Bay - Lady's Bay".
He wants a Māori name added too, in line with Auckland Council policy, and a separate sign explaining the history of the names.
"I understand that this bay was well known in Māori history as a landing place for canoes and was once the scene of spirited combat, and had a Māori name: 'Te Kuwata-O-Rangitaua'."
"Local iwi should be asked if this name is appropriate for the bay, or another more suitable name be agreed."
Travel advice site tripsavvy.com has Ladies Bay on its list of Auckland's best nude beaches, but also warns that it has developed "an unsavoury reputation in recent years and is no longer recommended".
Davis said there had been complaints in the past from local residents "offended by the sight of some of the men bathing there".
He had tried to get a "pre-warning" sign put up to advise bay visitors what they might see, but council staff didn't support the idea.