"I don't have a problem with the culvert as such, I'm more upset about the relevant hapū representatives not being part of the consultation and naming of the area," Matthews said.
Last year the Age reported on the issue in December, where Matthews was threatening to action an injunction to stop work on the culvert until the name had been changed.
Matthews said he had since decided to retract his decision to enact the injunction, as it was not his goal to stop construction, only to resolve the culvert's name.
He said it was important to address the issue now to avoid the hapū having to apply to change the name through the Waitangi Tribunal later.
The project is funded through the Government's shovel ready Crown Infrastructure Partners (CIP) programme, secured by former Minister for Regional Economic Development Shane Jones.
Jones said the Papakawau project was positive for the community and it was important there were no further delays.
"This project is for the entire community, not for a splinter group of Karahu crunchers who should conduct their debates on the marae and not the roadside," Jones said.
"The community is anxious for the project to be completed for the benefit of our harbour environment."
Waka Kotahi NZTA was approached for comment but did not respond in time for the edition.
The project is expected to be completed in April.