Looked up the full names of their sons:
Alexander Erik Hubertus Bertil
Alexander: personal preference?
Erik: Sofia's father
Hubertus: one of Carl Gustav's middle names
Bertil: CP's godfather and one of his middle names
Gabriel Carl Walther
Gabriel: personal preference?
Carl: first name of both Gabriel's father and paternal grandfather and CP's maternal grandfather (although he was known by his third name)
Walther: (third) name of CP's maternal grandfather
So, I'm guessing probably 3 names again with the first name based on personal preference and middle names more traditional and in reference to family members.
Boy: Ferdinand Andreas Gustaf
Ferdinand as the unexpected -but still rather traditional- first name (I also liked the idea of a prince Lars but that would be rather short in comparison to his brothers; both Lars and Ferdinand can be found in Sofia's family tree but only once). Andreas in reference to both CP's godfather and Sofia's great-grandfather. Also hoping for a Gustaf this time; so, all three are named after the king... If they'd like to be a little more original they could pick 'Folke' instead - but that would be two names with an F. I doubted about including Oskar (or Oscar) in the name as it would fit nicely with both sides of the family but as there already is a cousin Oscar, it's probably not the most likely pick.
Girl: Ingrid Renate Britt
In both cases the grandmother's second name; 'Britt' is also the name of Sofia's maternal grandmother; Estelle is already used Silvia, so I figured that Renate might be nice instead, although I wouldn't surprised if they use Silvia none the less) - as I've no idea what they might pick as a first name (I would never have guessed 'Gabriel' to go with 'Alexander') I decided to stick with Ingrid which is a name that can be found in the larger family tree of CP and of Sofia (with both Ingrid and Ingegerd - which to me look a lot a like but maybe that's not the way it is perceived in Sweden).
For those interested in the family names on Sofia's side of the family (information taken from
link (website seems a bit sketchy but the information seems legit). Names that occur more than ones (in whichever spelling are in bold).
Paternal side:
Father:
Erik Oscar
Paternal grandfather: Stif Ingvar
Paternal grandfather's parents:
Erik Andreas Emanuel & Frida
Kristina
Great-grandfather's parents: Anders
Fredrik &
Anna Charlotta
Great-grandmother's parents: Joel
Fredrik & Johanna
Paternal grandmother: Ingrid
Ann-Marie
Paternal grandmother's parents:
Oskar Petrus & Lily
Kristina
Great-grandfather's parents:
Karl Ferdinand & Hedda Vilhelmina
Great-grandmother's parents:
Carl August & Emma Helena
Maternal side:
Mother: Marie
Britt
Maternal grandfather:
Janne Herbert Ribbe
Maternal grandfather's parents: Lars Gotthard &
Maria Elisabet
Great-grandfather's parents:
Jan Persson &
Anna
Great-grandmother's parents:
Per Johan & Gum
Anna Maria
Maternal grandmother:
Britt Ingegerd
Maternal grandmother's parents:
Per Gustaf &
Grund Anna Maria
Great-grandfather's parents:
Per Gabrielsson & Hilma Maria
Great-grandmother's parents:
Grund Erik Johan & Knif Ida
Maria