The newborn heir is named HRH Princess Ingrid Alexandra. This is a name which honours Norwegian tradition, the family of HRH the Crown Princess, the history of the modern Norwegian Royal Family, and also pays homage to Norwegian history and the strong bonds of friendship and family between the Royal Family in Norway and the Royal families of Denmark, Sweden, and the United Kingdom of Great Britain and Northern Ireland.
Background of the name Ingrid
Ingrid is an ancient Norwegian name. It is composed of two parts - Ing(e)-, from the ancient Norwegian god-name Ing/Yngve, and -frid, meaning "beatiful (woman)". It was common in Norway all through the Middle Ages, up to modern times.
Once before there has been a Queen Ingrid in Norway - Queen Ingrid Ragnvaldsdatter, who was the queen of Harald Gille from 1134 to 1136, when he was assassinated. She was the daughter of King Ragnvald of Gothia (Götaland). The choice of the name Ingrid also pays homage to the Swedish and Danish Royal Families, as well as to the Crown Princess' father. The late mother of Denmark's Queen Margrethe II, Queen Ingrid, relict of Frederik IX, was the daughter of Sweden's King Gustav VI Adolf. The mother of Sven O. Høiby, father of the Crown Princess, was also named Ingrid.
Background of the name Alexandra
Alexandra is the female variant of Alexander, from Greek Alexandros, composed of the verb aléxein, which means "to protect, guard, aid", and the noun aner, which means "man, human". Technically speaking the letter "e" in aner is an "e macron acute", if I interpret my printed source correctly - I don't know any way to represent that in HTML - I think even Da'ud notation doesn't cover this particular peculiarity.
The choice of the name Alexandra reflects on the close links between the Norwegian Royal Family and the British and Danish Royal Families. King Olav V, dead 1991, was the son of the first King of independent Norway in modern times, King Haakon VII. He was not born with the name Olav, however. When Prince Carl of Denmark, son of Frederik VIII and grandson of Christian IX, accepted the Norwegian throne, and took the name Haakon, he decided that his 2 years old son, Alexander Edward Frederik Christian should be named Olav, as heir apparent to the Norwegian throne. The mother of Olav V was Queen Maud, who was born Princess Maud of the United Kingdom - she was the daughter of King Edward VII and Queen Alexandra, herself born Princess Alexandra of Denmark, daughter of Christian IX.
Only slightly related trivial information
As a matter of trivial information, in the decade prior to the First World War, the British Royal Family had two Royal Yachts. The larger was HMY VICTORIA AND ALBERT, of 4700 tons displacement - it was the official yacht of state of the United Kingdom. The British Royals did not like that vessel too much, and for more private uses they much preferred the vessel HMY ALEXANDRA, named for HM Queen Alexandra, and of less than half the displacement of the other yacht. As steamyachts of that time were want to have, she had a clipper-bow with bowsprit, elliptical counter-stern, two enormous steamship-funnels, and raked masts with rigging.
Following the Great War, this vessel was laid up, but in the early 1920s, it was sold to the Norwegian steamship-company Nordenfjeldske Dampskibsselskab (NFDS), which renamed the vessel DS PRINS OLAV, in honour of the Heir Apparent, and in accordance with that company's tradition of naming their ships for modern and ancient Norwegian royalty and great noblemen. In service with NFDS, DS PRINS OLAV was used as a luxury cruiseship, and it was hardly changed from its days as a Royal Yacht - one of the great attractions was that it was still possible to stay in the actual Royal quarters. Following the crack at the New York Stock Exchange, the vessel was inactive - there were rather few people who could (or felt they could) afford luxury cruises at the time - and was laid up until 1937, when the vessel was given a radical rebuild. Following the rebuild the vessel was completely unrecognisable, but was now a thoroughly modern passengerliner, and was employed in Hurtigruten, the express mail-, passenger-, and cargo-service between Bergen and Kirkenes. In 1940, the vessel was sunk by aircraft-bombs.
I am pleased with the choice of name. It strikes a good balance between honouring the distant past, honouring the recent past, and honouring the present, and it is nice name in its own right, striking a balance between being rooted in Norwegian traditions for names, and more modern influences.