A girl will almost certainly have Elizabeth as a middle name. I'm guessing that like August at least one name will come from Jack's side as well.
What about something from the Bowes-Lyon side...Cecilia Elizabeth Something for a girl. Celia, a nickname for Cecilia, was the name of Jack's paternal grandmother.
For a boy I wouldn't be surprised if one of Jack's late father's names were included...George Edward Hugh. As Andrew also has Edward in his name, Andrew Albert Christian Edward, it would be an easy way to honor both grandfathers.
I like the names Jack and Genie used over Bea's choice of Sienna.
I agree, they will use Elizabeth as one of the middle names if it is a girl.
I like the name Cecilia, that would honor both Genie and Jack's families. The Queen Mum's maternal grandmother was Caroline Louisa Burnaby, and Caroline would be a nice name too.
Then of course there is Alice for Prince Philip's mother.