How would the Crown change New Zealand’s name to Aotearoa in order to help restore the status of the Māori language?

CNN’s Māori Party campaigns to change New Zealand’s name to Aotearoa links to Maoriparty.org’s petition Change our official name to Aotearoa.

The Crown is mentioned in two paragraphs of the petition’s statement:

Name changes over our whenua and the imposition of a colonial agenda in the education system in the early 1900s meant that Te Reo Māori fluency among our tupuna went from 90% in 1910 to 26% in 1950. In only 40 years, the Crown managed to successfully strip us of our language and we are still feeling the impacts of this today. It’s totally unacceptable that 20% of the Māori population and 3% of people living in Aotearoa can speak te reo Māori.

and

It is the duty of the Crown to do all that it can to restore the status of our language. That means it needs to be accessible in the most obvious of places; on our televisions, on our radio stations, on road signs, maps and official advertising, and in our education system.

Question: What is the process the Crown would follow to change New Zealand’s name to Aotearoa in order to help restore the status the Māori language? Would this actually be done by public referendum, or would it really be up to the Commonwealth to implement the name change?