Members of the media in the United Kingdom suggest that for the family of Pippa and James each of the names has a special significance.
The 35-year-old's choice of moniker is a nod to her brother-in-law Prince William as well as two other family members.
Meanwhile, James Matthews chose to honour his brother, Michael Matthews, who died at the age of 22 in a tragic accident climbing Mount Everest back in 1999.
The socialite gave her profession as "author" on the birth certificate, according to the Mail on Sunday.
Pippa Middleton and husband James Matthews have picked a very special name for their firstborn child.
Her party-planning book Celebrate was published in 2012. The happy couple have yet to officially announce any details about their new bundle of joy, except for these recent reports on their baby name.
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Anglophiles would know that Arthur is the middle name of three renowned royals: Prince Charles, the little one's first cousin, Prince Louis, and his uncle, Prince William.
Just like her big sister Kate, Pippa gave birth at the private London Hospital, but the news of the birth wasn't made public until October 16.
Just days earlier, Middleton attended Princess Eugenie and Jack Brooksbank's star-studded Windsor wedding. "Everyone is delighted and mother and baby are doing well".
35-year-old younger sister of Duchess Kate Middleton first became a mother almost a month ago, up to this time her son's name is kept secret.
He was clutching a duffel bag likely containing much-needed supplies to help the young family prepared for their second night as parents.