During a pre-recorded interview for Saturday night's Jonathan Ross Show, the singer and reality star revealed: "We have four names. Maybe you can help me out actually.
"We had Rose. I love Rose because it's English and beautiful. "Ameila, beautiful name. Elizabeth. Alexandra. So these are the four names that we've been throwing around. I love them because they are English and they are beautiful."
Peter added: "The baby came three weeks early. Then we looked at each other and I said, 'We haven't got a name,' so we started calling her Rose, but she wasn't a Rose.
"It didn't click. So then we went backwards and forwards. Then three days ago she (Emily) throws another spanner in the works and says, 'What about Poppy?' Poppy is a nice name.
"Then she threw in Isabella and I thought that's a nice name. So we're sort of in a bit of a pickle here."
Peter, 40, who is already dad to Junior, eight, and Princess Tiaamii, six, his children with his former wife Katie Price, went on: "I've had two children, biological children, and this is her (Emily's) first, so I want her to be happy. My favourite is Ameila. I love that name but I want her to be happy.
- OK! Magazine (@OK_Magazine) January 27, 2014
Chat show host Jonathan also asked Peter when his wedding would be.
Peter revealed: "I said about two years. I believe in the institution of marriage but there's so many people who have been together with their partners twenty, thirty years and never got married and that's fine, that's perfect.
"In my case, I want to get married eventually, but I'm in no rush. What I wanted was the engagement. It's so important for me. She's got to finish her degree at the end of this year, then she'll be a fully qualified doctor. Let her do her F1, then we'll get married and then we'll have another baby.
"I want to do a traditional English wedding, to the finest detail. Then I want to go to Cyprus and we want to smash plates."
See the full interview on the Jonathan Ross Show, Saturday 1 February at 9.35pm on ITV.
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