Council officers assessing the application against the street-naming policy apparently quite liked the name but could not recommend it to the council.
Under the policy, names should have "significant local content or meaning" and should not be confused with streets with similar names.
Officers said Cotterville Lane could be confused with Cotter St and recommended the council approve the name Flax Mill Lane.
Early settler Pierce Cotter, who Cotter St is named after, established a large flax mill on the land towards Woodside which was known as Riverside.
The old mill, now a woolshed, remains in Monty's Lane.
Councillors voted to approve the name, provided it was supported by the Greytown Community Board. They also moved to amend the policy so all street naming be referred to community boards in the first instance for a recommendation.