Council chief executive Michael Day confirmed the page had been incorrectly titled and said it needed to be changed.
First-term councillor Barry Stewart then interjected.
“Are we going to reverse all these European names and put the Māori names first on everything? Because I’m going to object every time.
“Evelyn’s busy saying — I’m presuming she’s saying — that the Māori name should be above.”
When a councillor sitting next to Stewart confirmed it was the name of the museum, he responded “I didn’t agree to it”.
Chairman Tom Campbell clarified the museum’s collection had a te reo name, which needed to be reflected in the report, while Cook said it was a matter of consistency.
“If we are going to be consistent with decisions we have already made at this table, then the documents we produce should also reflect that,” she said.
Stewart was elected in 2022 as the 12th and final councillor by a margin of 26 votes.