Jenny Åkerström is credited as the originator of the recipe. Åkerström was a Swedish home economics guru at the beginning of the 20th century and was even an instructor to the three Swedish princesses, Margaretha, Märtha, and Astrid, daughters of Prince Carl (brother of King Gustaf V). She published a four volume series of cookbooks called Prinsessornas Kokbok: Husmanskost och Helgdagsmat (Princesses Cookbook: Home Cooking and Holiday Food). The first edition came out in 1929 with the princess’ portraits gracing the cover. With it’s great success came eighteen reprints with revisions up through 1952.
I wasn’t able to find any definitive information about why the books were called the princess cookbooks or why the princesses agreed to have their images on the cover other than the fact that Jenny Åkerström was their teacher and the princesses were seen as role models. Their education included child care and cooking which was innovative at the time. In a feminist sense, formal domestic training highlighted the professionalism required to manage a home and children.Korena Vine of Korena in the Kitchen gives more details on the origin of the name of the cake as well as beautiful pictures of it:
One story is that this later became known as “princess cake” (prinsesstårta) because the three princesses are said to have loved it so much. Another story is that Ms. Åkerström actually created three very elaborate “princess cake” recipes – a different one for each princess – and that the current version is a simplified combination of all three. That explains the princess connection, but the reason for the cake being green still seems to be a mystery. Today, prinsesstårta is popular in Finland as well as Sweden – so much so that the third week in September is officially Prinsesstårta Week!