I'm really excited to find out the name!
I expect it will be something really really traditional.
Seeing as the child will be placed after Prince William in the line of succession and therefore will be an heir, it's almost 100% certain that his/her name will be top-traditional.
First name: They could choose to go with the ultra traditional names like George, Richard or Edward; Elizabeth, Victoria or Mary. Or they could go with more uncommon yet traditional names like Arthur, Philip, Alexander or Albert; Charlotte, Matilda, Alexandra or Margaret. My money are on either George or Arthur, or Elizabeth, Margaret or Victoria.
"Middle names": As with (almost) every royal baby, the secondary names are probably going to get used to honour family members. A strong contender in my opinion is Francis/Frances, in a girls name being a replacement for Diana. Frances was Diana's middle name and Francis is Michael Middleton's middle name. Francis furthermore has a royal connection in that the father of Queen Mary, the grandmother of Her Majesty the Queen, was Francis, the Duke of Teck. Family names used could be, for a boy: Charles, Louis, Michael, James, Arthur or Philip, for a girl: Elizabeth, Margaret, Anne, Alice, Diana, Alexandra, Carole/Caroline or Mary.
My (first) guesses for a boy:
George Charles Arthur Philip
Arthur Charles Philip Francis
George Philip Arthur Michael
Alexander Philip Arthur George (long-shot)
Albert Michael Charles Philip (long-shot)
My (first) guesses for a girl:
Elizabeth Alice Caroline Frances
Elizabeth Carole Mary Diana
Margaret Caroline Frances Elizabeth
Victoria Carole Diana Elizabeth
Alexandra Elizabeth Caroline Frances (long-shot)
Mary Elizabeth Carole Diana (long-shot)
Alice Diana Elizabeth Carole (long-shot)