The couple's first child together will be named Bear and will take his mother's last name, Winslet.
“They are all doing so well, they both absolutely adore him -- and the name Bear,” an insider told British newspaper The Sun.
Bear Winslet was born on Dec. 7 at NHS Hospital in Sussex County in England.
This is the third child for Winslet, 38, who has two children from her previous marriages. A 13-year-old daughter, Mia Honey, from her marriage with producer Jim Threapleton and a 9-year-old son Joe Alfie with director Sam Mendes.
The Academy Award winner married Rocknroll in a secret ceremony in New York 12 months ago.
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