Leonore, who was born on 20 February and is fifth-in-line to the throne, will have the title of Duchess of Gotland.
The name Lilian is a likely nod to the late Princess Lilian of Sweden who passed away aged 97 in March last year, while Maria may be in honour of Chris' mum Eva Maria. Leonore is also reminiscent of Spain's future queen, eight-year-old Infanta Leonor.
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"It's definitely something new," royal expert Roger Lundgren told the Aftonbladet newspaper immediately after the announcement. "There aren't many Swedish girls called Leonore." The moniker is in fact only held by 128 women in Sweden, according to national statistics.
Shortly after Princess Madeleine gave birth in New York, her parents King Carl and Queen Silvia flew stateside to meet their baby granddaughter. As soon as they heard about the new arrival last week, the reigning monarchs shared their congratulations with Madeleine and Chris.
"We know today both happiness and warm thanks," said King Carl and Queen Silvia. "Our joy is great. We wish now that Princess Madeleine and Christopher get peace and quiet and can take advantage of this unique time with her little daughter."
As keen users of social media, Princess Madeleine and Chris have kept followers updated with news about their royal darling.
Madeleine shared a photo of the couple leaving the hospital with their newborn on her Facebook page last week. In their first family snapshot made known to the public, the princess and her London-born husband are pictured standing in the corridor of the hospital, with their daughter sleeping in a car seat gently covered with a blanket.
"She looks like her mum which is all I wanted," Chris had previously said about his baby. "We have ten fingers, ten toes. And she's got a very strong, nice roar on her."
Madeleine and Chris live and work in New York — the city they have called home for several years. The princess works for the non-profit World Childhood Foundation, founded by her mother, Queen Silvia.