Dutch Crown Prince Willem-Alexander has named his new baby daughter Catharina-Amalia Beatrix Carmen Victoria.
The prince was inundated with messages from well-wishers
The princess, who was born on Sunday, is second in line to the throne and will be known as Amalia for short.
As he arrived at the register office in the Hague, the prince was greeted by a crowd of hundreds of well-wishers.
He drank toasts with the city's mayor and Dutch Prime Minister Jan Peter Balkenende, who acted as a witness at the ceremony.
The birth has been widely celebrated - many people hung out banners in orange, the royal colour, from their homes.
Others inundated the royal website with messages of congratulations.
The Crown Prince said his wife, Argentine-born Princess Maxima was doing well and was "intensely happy".
He said Amalia "eats well, sleeps well, and cries well when she is hungry".
The 3.3kg (7.3lb) baby is likely to become Queen Amalia because boys and girls have equal succession rights in the Netherlands.
The names Beatrix and Carmen are taken from her grandmothers, Queen Beatrix of the Netherlands and Carmen Zorreguieta.
Her titles are Princess of the Netherlands and Princess of Oranje-Nassau.
The royal couple married in Amsterdam in February 2002.
Their easy-going manner has made them a big hit with the Dutch public.
Tens of thousands thronged the centre of Amsterdam for the wedding.
The bride's father was not permitted to attend because he had held a government position during Argentina's military dictatorship.
Prince Willem-Alexander's younger brother, Prince Johan Friso, has given up his right to the throne s a result of a controversy over his fiancee's previous contacts with a criminal.