Willem-Alexander announced the name as he went through the formality - as all Dutch parents must - of registering his daughter at city hall.
Unlike other Dutch parents, Willem-Alexander was accompanied by Prime Minister Jan Peter Balkenende as he registered his daughter, who was born Tuesday night and is fourth in line to the Dutch throne.
Wilhelmina is the name of current Queen Beatrix's grandmother, who ruled the country from 1898 until 1948, including leading the House of Orange in exile in London during Nazi Germany's World War II occupation of the Netherlands. Wilhelmina died in 1962.
Ariane's two sisters are called Amalia and Alexia.