As well as the international majors, are local car rental companies.
https://www.omegarentalcars.com/car-...hurch-airport/
https://www.apexrentals.co.nz/rental...airport-branch
https://www.ezicarrental.co.nz/locat...hurch-airport/ Was know as A2B Car Rental
An others. But avoid the "rent a wreck" very low cost places, with ~10 year old cars.

You may pay a premium to rent from the airport. Renting from a city location may be a lot less, for the small cost of a taxi/uber from the airport to the rental car location.

Edit
Other smaller rental companies (alphabetical order)
https://www.acerentalcars.co.nz/
https://www.arentals.nz/
https://www.gorentals.co.nz/
https://www.radcarhire.co.nz/