I think the second baby will have same naming pattern as August:
August (from maternal great x5 grandfather) Philip (from maternal great grandfather) Hawke (from paternal great x5 grandfather)
The pattern is one name from close senior relative (pretty sure it'll be George if a boy and Elizabeth if a girl), and other two names from both sides for the families that are symmetric. Also to me it seems like if they chose name from a distant ancestor they preferred someone significant or with certain achievement (like P Albert and Hawke who was a Reverend and a JP), rather than just simply choose a "sound good" name.
Boy,
Ivor - from maternal great grandfather (a Brigadier)
George - from paternal grandfather
Godfrey - from paternal great grandfather (a Captain, fought in WWII)
Herbert - from maternal great x3 grandfather (a Lieutenant-Colonel, fought in WWI)
George - from paternal grandfather
Thomas - from paternal great x3 grandfather (2nd Earl of Leicester)
I think it's a boy BTW.
Girl,
Alice - from maternal great x2 grandmother
Elizabeth - from maternal great grandmother
Olive - from paternal great x2 grandmother
Celia - from paternal great grandmother
Victoria - from maternal great x5 grandmother (also Eugenie's own middle name)
Elizabeth - from maternal great grandmother