Lanford Beard
July 11, 2011 AT 09:30 PM EDT

Two days after giving birth to a son with fiancé Matthew Bellamy, Kate Hudson and the Muse frontman are still contemplating the baby’s name, reports People. Hudson delivered the 7-lb., 12-oz. baby on Saturday night and plans to recover in Los Angeles. After that, she and her rocker hubby-to-be set down roots in London, where U.K. native Bellamy will work on Muse’s sixth studio album. This is Hudson’s second son. She delivered seven-year-old Ryder Russell Robinson while married to her ex-husband and Black Crowes frontman Chris Robinson.

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