Why a Hanoverian/Windsor name?
The Mountbatten-Windsors don't seem to place much emphasis on the use of Hanoverian/Windsor names. Of the Queen's children, two had Stuart names, one had a Greek Royal name, and one had a name that has been seen in almost every house (the exceptions being the Normans, Stuarts, and technically the Hanovers). Of Charles' children, both have names that heavily predate the Hanovers - William is seen in the Normans, Stuarts, and Hanovers, while Henry is used by every house from the Normans to the Tudors.
If we're thinking that it's going to be a monarch's name and limiting it to just the Hanovers/Windsors then we're left with George, William, or Edward for a boy and Victoria or Elizabeth for a girl. Because I highly doubt they're going to go with a name already in use (except for maybe the Queen's), that leaves George, Victoria, and maybe Elizabeth. While I have nothing against any of these names, I really hope they don't go with George simply because it's been too over used in recent history, and I hope they don't go with Elizabeth because it puts too much pressure on the child - who will doubtless be compared to her great-grandmother and grandmother regardless of name.
I'm hoping that this child has the name of a pre-Hanover monarch. A Richard or Stephen if it's a boy and we're looking at just English names that aren't in use, although I wouldn't rule out Charles either. Then Mary or Matilda if it's a girl.