Seeing how I have nothing to determine their taste in names, other than their dog's name ... I'm totally just gonna make guesses entirely based on the fact that they named their dog Siri and presumably like that name.

So short, simple, Scandinavian, and both traditional and currently popular. And to go with Victoria's and Madeleine's kids, predictable middle names with more focus on close family than on old royal ancestors. All right.
Boy: Prince
Axel Carl Erik Bertil
Girl: Princess
Greta Silvia Marie Lilian
Duchy: Dalarna
Godparents:
Crown Princess Victoria
Lina Hellqvist
Frida Vesterberg
A friend of Carl Philip
Some male royal probably
Other first names I considered:
Alvar, Arvid, Bertil, Carl, Folke, Gustaf, Hugo, Ludvig, Olof, Oscar, Vidar, Wilhelm
Alma, Alva, Astrid, Disa, Ebba, Hedda, Ida, Ingrid, Matilda, Märta/Märtha, Saga, Signe, Tyra/Thyra
(And a couple of years ago I would definitely have said Elsa, but, you know ...)