Plunket is a core partner supported by BNZ, who had suggested Williams carry the logo of the community organisation in the space on the collar of the playing jersey.
BNZ chief executive Anthony Healy said, "As we said on the weekend, we understand that Sonny Bill's objection to our logo on his jersey is based on his faith.
"Yesterday, we put an idea to him as an alternative to the BNZ logo on his jersey.
"We are delighted that Sonny Bill has agreed to give the space, previously allocated to BNZ, to another of our core sponsorships, Plunket, who provide a vital support service for children and new parents.
"We think this is a fantastic outcome for all."
Williams will make his first start of the season at second-five in the only change from the side that lost in Dunedin. Rieko Ioane will start alongside Sonny Bill at centre, which sends All Black George Moala back to the bench.
The Blues team is:
1 Pauliasi Manu, 2 James Parsons (C), 3 Charlie Faumuina, 4 Gerard Cowley-Tuioti, 5 Scott Scrafton, 6 Jerome Kaino, 7 Blake Gibson, 8 Steven Luatua; 9 Augustine Pulu, 10 Piers Francis, 11 Melani Nanai, 12 Sonny Bill Williams, 13. Rieko Ioane, 14 Matt Duffie, 15 Michael Collins.
Replacements: 16 Matt Moulds, 17 Ofa Tu'ungafasi, 18 Sione Mafileo, 19 Jimmy Tupou, 20 Akira Ioane, 21 Billy Guyton, 22 Bryn Gatland, 23 George Moala.