Kim Kardashian and Kanye West have named their baby daughter North West, according to reports.

The 32-year-old E! reality star and her 36-year-old rapper boyfriend, are believed to have already given their 5-day-old little girl the nickname 'Nori', according to UsWeekly.

Meanwhile, TMZ are claiming to have witnessed a signed birth certificate with the name North West, signed by both parents.

It was previously suggested that the celebrity couple would continue the 'K' theme that runs in Kim's family with the name, Kai Georgia Donda West, being in the running from fans and the media earlier in the week.

Kim's due date was July 11, but she gave birth five week prematurely on June 15.