The engaged couple welcomed their son over the weekend after Kate gave birth naturally, despite having has first son Ryder, seven, via a caesarean section.
But according to People magazine, the Muse frontman and the actress can't settle on a name for their baby, who weighed in at 7lbs 12oz.
A source said that Kate was doing 'great' and the couple were 'beyond thrilled' with their bundle of joy. They now plan to recuperate in Los Angeles before settling in London so that Matt can work on his band's next album later this year.