The choice of the name Michael has special significance as James' brother Michael was aged 22 when he disappeared during a Mount Everest expedition.
The couple have also given their baby boy the middle names Michael and William.
Baby Arthur's middle name might be a tribute to Pippa's brother-in-law.
Pippa gave birth in the Lindo Wing at St Mary's Hospital in West London, the same place her sister Kate gave birth to all three of her children - George, Charlotte and Louis.
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The Mail cited the child's birth certificate, and we have an idea of how they chose the baby's three-part moniker. The name of Michael's wife gave the boy in honor of the family.
We know that Middleton and Matthews' baby will likely have many play dates with his older cousins but he will be bonded with the youngest of the Cambridge children in a unique way. Michael is also the name of Pippa's father. Middleton gave birth to Arthur in October just hours before Meghan Markle's pregnancy was announced by Kensington Palace.
Matthews was spotted running into the hospital on the day after the birth apparently in the same clothes he arrived in the day before.