Now, the new parents have named their newborn son Bear Winslet, a rep for the 38-year-old actress confirmed to ABC News.
Winslet welcomed her third child Dec. 7 at a hospital near the West Sussex, England, home she shares with her husband and two other children, Mia, 13, and Joe, 10.
Rocknroll, 35, who works on his uncle Richard Branson's Virgin Galactic project, was previously called Abel Smith before changing his name.
Bear Winslet is not the first celebrity offspring to hold that moniker. Alicia Silverstone's 2-year-old son is named Bear Blu.
Winslet recently responding to criticism that her children, who all have different fathers, are shuttled between her and her exes. The Oscar-winner told the November issue of Vogue, "They've always been with me. They don't go from pillar to post; they're not flown here and there with nannies."
"That's never happened. My kids don't go back and forth; none of this 50/50 time with the mums and dads - my children live with me; that is it. That is it!" she added.