Princess Beatrice and husband Edoardo Mapelli Mozzi welcomed their baby daughter at 11.42pm on September 18. She is the couple's first child. Edoardo has a four-year-old son named Wolfie from a previous relationship. Sienna will receive an official title, passed on by her father's family as they are part of the Italian aristocracy.
Speaking on Podcast Royal, Jessica Rachel Burchfield and Jessica Robinson discussed the new name.
They said: "Sienna Elizabeth Mopelli Mozzi pays homage to Beatrice's grandmother, Queen Elizabeth.
"As well as, apparently, Beatrice's red hair.
"A source told HELLO! that they were looking for an Italian name which started with an 'S' for Sarah, to honour the Duchess of York."
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Ms Burchfield added: "It also reflects the golden rust colour of Beatrice, the Duchess of York and the baby.
"I guess the baby is a little redhead which is so cute.
"The oddsmakers were kind of right, the first name did end in an A, and was Italian inspired and Elizabeth was included.
"Sienna does have a royal title but it's not from the British Royal Family.
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"Edo, Beatrice's husband is from Italian aristocracy."
The title Sienna receives will be "nobile donna, "which translates to "noblewoman."
Count Alessandro Mapelli Mozzi, Beatrice's father-in-law explained the reasoning for the title to the Daily Mail.
He said: "Edoardo is the only male descendent taking the family into the next generation. He is a count his wife will be a countess automatically and any of their children will be counts or nobile donna."
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This week Beatrice was seen publicly for the first time since Sienna was born.
The smiling Princess Beatrice looked as she was enjoying motherhood as she took Sienna, the Queen's 12th great-grandchild for a walk in London.
Royal births have boomed this year. In February, Beatrice's sister Eugenie and her husband Jack Brooksbank welcomed baby August.