Kim Kardashian and Kanye 'battle' over daughter's name - North West or Kaidence Donda West

It sounds like the punchline to yet another Kardashian joke. But new mother Kim is said to be seriously considering naming her first child 'North'.

With the child taking her father Kanye's surname the youngster would be 'North West'.

But it is not the only name in consideration, with Kim said to prefer the choice of Kaidence, which would follow her family's 'K' theme.

The reality star is said to like the idea of calling the baby Kai for short. The middle name would be Donda, in honour of Kanye's late mother.

But according to InTouch: 'North is at the top of the list of names'.

A friend of the pair told the gossip magazine: 'They're not totally sure about it. Kanye loves it, Kim is okay with it.'

Prior to the baby's birth on Saturday it had been expected that the pair would continue the 'K' theme that runs in Kim's family - something that Kaidence would fit.

Kim, 32, has mentioned in the past that it will likely begin with a 'K'.

And it seems her family are keen that remain the plan.

'The family doesn’t like it [North],' the insider told InTouch, adding, 'They're going to decide by today [Tuesday].'

Kanye has not spoken publicly following his daughter's arrival. But he did take to Twitter on Tuesday morning - to promote his new album Yeezus as it was released.

'Yeezus album now available,' he tweeted.

Despite his disagreements with Kim over the name, Kanye is said to be thrilled to be a first time father at 36.