Tatler reckons Kate and William's children will be called...

[LittleCheesyPineappleOne]

Mary and George (twins)
then David

(or so I was reading in the hairdresser today)

WDYT?

Caroline Diana for a girl (carol a nod to Kate's mum, but the more regal version of Caroline)

If you look back at their patterns of naming, they NEVER choose a name from recent relatives - only past, historic.

I would say Philip is a strong contender for a boy's name, whether first name or subsequent.

Albert
Edward
Alfred
Leopold
Charles
Louis
Alexander
James

Adelaide
Mary
Alice
Victoria
Helena
Caroline
Frances
Alexandra
Anne or Anna
Julia
Margaret

Plus Diana but probably not as a first name, and possibly Catherine as a second or third name too

In case you are reading, William and Catherine, to include Philip and Elizabeth would be cool, you probably should stick Charles in too.
I think your first born should be called either Helena/Eleanor/Anna if a girl, and perhaps Edmund (Ned), Edward (Teddy) all are very classic and would go well with the middle names you'll have to use (you will have to use Diana).
I think as you live in Wales and are going to be Prince of Wales one day you must include a Welsh name, with the Welsh spelling, consider using, Owain, Gethin, Gareth Daffyd ,Huw,or for girls Medi, Myfannwy, Morwenna, Alis, Eirlys, Ffion, Angharad

James is the Wessex boy so that's out IMO.

Meant to add that Philippa for a girl is possible.