Councillor Larry Baldock said it had been a "mistake" for the council to consult on that name.
He said naming things was a leadership function and consultation just "made a mess of it". There was a risk councillors would support the majority view rather than doing what was right and potentially removing a name that was offensive to tangata whenua.
"We have to name things, that's what this council does."
Robson said the name was the victim of a poorly managed project, not of one bad consultation.
"We didn't do proper engagement, we just dropped the name on people and associated it with a project that was a cluster bubble."
Consultation was not a referendum, and elected members could vote against the majority view, as he had in supporting the new name.
Councillor Max Mason said some in the community felt a "fear" about Māori names.
"It's the elephant in the room."
He said the council needed to communicate clearly in order to prevent misconceptions and prejudices from taking hold.
The draft policy would also put a stop to the practice of allowing people to make private requests to have street names changed.
The council would still be able to hear submissions from the community on renaming proposals and decide whether or not to follow them up.
The new policy also allowed for both new and existing streets, reserves, facilities and public places to be given dual names in both English and te reo Māori.
There were already examples of this in Tauranga, such as the Gate Pā Domain, also known as Pukehinahina.
Under the draft policy, the Māori name would come before the English name.
Tauranga's longest street name
Te Rua o Korotangi Roadway (26 characters)
Tauranga's longest reserve name
Maxwells Road Esplanade Reserve. This is the same number of characters - 31 - as the controversial Te Papa O Ngā Manu Porotakataka.