The former glamour model confirmed her baby's name in a magazine interview, saying: "We really struggled to decided on a name.
"It's really cute, isn't it? I considered it being spelt 'Bunni' with a heart above the 'i', but I don't think that's really a part of the English language!
"I love Duchess Kate, though, so I've told Kieran that if we have another daughter that will be her name! I think it goes well with Princess. She would have been Duchess Kate of Brighton!"
Bunny won't be alone in having an unusual name in her family.
Her big brother by dad Kieran is called Jett Riviera, and her mum's other kids are (by Peter Andre) Princess Tiaamii Crystal Esther, Junior Savva Andreas, oh and (by Dwight Yorke) plain old Harvey! According to our baby name generator, the name Bunny 'is a nickname derived from names such as Barbara and Bernice'.
It add: "It is a common name used for pet rabbits, and is also has ties to the infamous Playboy Bunnies."
While most of Katie's Twitter followers welcomed the new baby name, one offered this note of caution for the future....
Let's hope Katie Price's baby girl 'Bunny' doesn't marry someone with the surname 'Boiler'.
- Vicki (@xvlfx) September 15, 2014
And, of course, professional provocateur and names obsessive Katie Hopkins had her say, guaranteed to send the other Katie hopping mad:
What do you think of baby Bunny's name?
Bunny? BUNNY?! Makes sense I guess, given your dad was going at it like a rabbit with all of mums mates.
- Katie Hopkins (@KTHopkins) September 15, 2014