Kim's daughter with rapper Kanye West was born on Saturday - five weeks early and weighed just five pounds. No name has been announced, but ones starting with the letter K are favourite, reported Sun online.
Donda, after Kanye's mother who died in 2007, could also be in the running.
"She has dark hair and looks just like her mum," a source said.
Friends visited Kim, 32, in her 2,000 pounds-a-night LA maternity suite.
The newborn could even feature in reality show Keeping Up With The Kardashians - but Kanye is said to be dead against the idea.