The actress and fiancé Matthew Bellamy welcomed a son Saturday night

By Sarah Michaud
Updated July 11, 2011 02:10 PM
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Credit: Jason Merritt/Getty

Decisions, decisions.

Kate Hudson and fiancé Matthew Bellamy are still musing over what to name their new baby boy, born Saturday night, a source tells PEOPLE.

Luckily, they have a bit more time to decide – although the actress, 32, and rocker, 33, plan to settle in London while Bellamy’s band Muse works on their next album, they’ll remain in Los Angeles while Hudson recovers from the birth.

The Something Borrowed star – who delivered her 7 lbs., 12 oz. son naturally despite having undergone a Cesarean section with Ryder Russell, 7½ – is “doing great,” says the source, adding that the couple is “beyond thrilled” with their new addition.