I don't think this applies, because you could interpret INZ 1175 Section C as meaning, 'Who was your partner on the Residence application?' rather than, 'Who is your live-in partner now?' As long as this section matched with the original Residence application, I very much doubt anyone would give it a second glance, anyway. BUT... it's arguable.
Partner’s and children’s personal details
Only people included in the original resident visa application may be listed here.
C1 Partner
Family/last name
Given/first name(s)
Date of birth D D M M Y Y Y Y
Passport number
Expiry date D D M M Y Y Y Y
Country Relationship to applicant
Obviously, this would all depend on the terms you are on with your ex-partner, and your own gut feeling about what you should do. If you aren't happy about it, you'll need to tell INZ, apply individually, and supply evidence.