"A year ago when I got married to Willy Moon I took his last name. For a long time the friends and family closest to me have called me Teddy, and my husband decided it would be beautiful to spend the rest of my life with my most intimate name united with my new married name," Kills wrote.
"So for a year I have been Mrs Teddy Natalia Noemi Sinclair, and I've never felt so natural, honest and empowered ... And I'm finally ready to invite you all to address me personally as I feel we are so close and I am so grateful for your support and love."
In a subsequent post promoting the private Instagram account @whothehellisteddysinclair, Kills hinted she was changing her name because of all the negative comments she was getting on social media.
Kills and Moon fled New Zealand after the pair attacked contestant Joe Irvine over his outfit and performance of Cry Me a River, with Kills saying he had copied Moon's look.
Moon compared the Invercargill singer to a serial killer. Both were sacked by Mediaworks the following day, following a public outcry and disquiet from the show's sponsors.
In an exclusive interview with the Herald, Kills defended her comments, saying other reality show judges - including X Factor creator Simon Cowell - had said worse things.
Read more: Natalia Kills exclusive: Simon Cowell is a harsher judge than me
"I've been a fan of The X Factor and Simon Cowell my whole life and what we said is light compared to what Gordon Ramsay, Simon Cowell and many others have said on national television and been celebrated for," she said.
"It's so sad how they (TV3) encourage so much drama but then when their sponsor and the public react badly they release a statement branding us as 'bullies'."
- nzherald.co.nz