Princess Leonore is currently fifth in line to the throne, and was born at a hospital in New York last week.
One of her middle names comes from the late Princess Lilian, Madeleine's great-aunt, while Maria is one Chris O'Neill's mother's middle names.
Leonore is a very rare name in Sweden, just 35 women have it as their first name, news agency TT reports.
Alice Trolle-Wachtmeister, who serves as the senior lady in the royal household or the so-called Mistress of the Robes, says, "Isn't it it pretty 'in' in Sweden today to have a slightly unusual name? Not everyone can be called Pelle or Lisa."
The name Leonore will work just as well in New York as it will in Sweden, according to the name researcher Eva Brylla.
"It's international and easy to pronounce," she says.
Her mother's full name is Madeleine Thérèse Amelie Josephine, her father's is the simpler Christopher Paul.