The boy and girl were born three months ago but, in accordance to Danish tradition, did not have their names revealed until their christening at the Holmen's Church in Copenhagen yesterday.
According to the AFP, the children were baptised Vincent Frederik Minik Alexander and Josephine Sofia Ivalo Mathilda in front of 300 friends and family. It is believed that "Minik" and "Ivalo" are Greenlandic names, a nod to Denmark's autonomous territory.
At the service and the after-party at the Amalienborg Castle, Australian-born Princess Mary wore a royal blue dress with a cream head piece, while the babies were dressed in long, white lace gowns.
The couple already have 5-year-old Prince Christian and 3-year-old Princess Isabella.
Earlier this year, Princess Mary revealed that she had her "hands full" with the twins but felt very "proud and happy".