Jason Benade comes in at hooker, Prince Gaoseb at flanker and Le Roux Malan in the centre while Richard Hardwick switches to No 8 for the game in Toulouse on Friday.
Both teams lost their openers. Namibia went down 52-8 to Italy for a 23rd straight defeat at the World Cup. The only game they have not lost was an encounter with Canada four years ago, cancelled because of a typhoon.
New Zealand suffered a first ever group defeat as they lost their opener 27-13 to hosts France.
"The Italy game was a big challenge for us, especially in the set-piece. Hopefully it will be better," said Coetzee.
"We have to throw more punches."
"New Zealand is a top nation. Our plan is to stop the momentum and break their rhythm."
Namibia lost 71-9 to the All Blacks four years ago and 58-14 in 2015.
"We knew it was a tough pool," said Coetzee. "It is not scary but we really get excited about it. New Zealand are taking this game seriously. It is good for the competition. It is a great opportunity for our players."
Flyhalf Cliven Loubser added: "It is a great opportunity. When you grow up in Namibia, you want to play against New Zealand."
Namibia team to play New Zealand in Rugby World Cup Pool A match in Toulouse on Friday (Kick-off: 9pm CAT):
Cliven Loubser; Gerswin Mouton, Johan Deysel (capt), Le Roux Malan, Divan Rossouw; Tiaan Swanepoel, Damian Stevens; Richard Hardwick, Prince Gaoseb, Wian Conradie; Tjiuee Uanivi, Johan Retief; Aranos Coetzee, Torsten van Jaarsveld, Jason Benade
Replacements: Louis van der Westhuizen, Des Sethie, Haitembu Shifuka, PJ Van Lill, Adriaan Booysen, Max Katjijeko, Jacques Theron, JC Greyling
Coach: Allister Coetzee (RSA)
