Nicki on a female pet carries the unmistakable pull of Nicki Minaj, one of the most commercially successful and stylistically distinctive figures in hip-hop. Whether that's the explicit reference or not, the name reads with that energy: confident, unapologetic, commanding attention. It's not a subtle name, and that's the point.
The Nicki Minaj Effect
Nicki Minaj's dominance in pop and hip-hop from the late 2000s onward made this spelling distinctly hers. Pet owners choosing Nicki with the I spelling are almost certainly nodding to that reference. It suits bold, personality-forward dogs: Chihuahuas with maximum attitude, or Dobermans who own every room.
Sound Fit
NICK-ee is two syllables with a sharp opening consonant that cuts through noise. It's a good recall name for energetic dogs. Bright and assertive without being harsh.
Counter-Reading: Locked to One Reference
Nicki with this spelling is so strongly associated with the rapper that the name carries all of her cultural context. If you want the sound without the celebrity attachment, Nikki with double-K is more neutral. See also Nicole for the formal origin context behind the nickname.