The star became a dad for the third time earlier this year, but he and fiancée Emily MacDonagh have yet to tell the world the name of their new arrival.
Pete told the chat show host: ‘We have four names. Maybe you can help me out actually… We had Rose. I love Rose because it’s English and beautiful.’
‘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 any forwards. Then three days ago she (Emily) throws another spanner in the works and says, 'What about Poppy?' Poppy is a nice name.’
He said: ‘Amelia, beautiful name. Elizabeth. Alexandra. So these are the four names that we've been throwing around.’
The singer continued: ‘I love them because they are English and they are beautiful.’
Pete and Emily introduced their baby daughter earlier this month following the newborn’s dramatic arrival.
The couple were stuck in traffic as they made their way the hospital. Emily had been in labour for 4 hours by the time they arrived.
Pete had previously said he was keen on more traditional names, it would seem that the couple are still planning to stick to a more conventional name for their new daughter.