I can't resist joining in on the naming fun as there are so many interesting factors and traditions with royal naming practices. From my research, the first name will likely be that of a former King or Queen who served on the throne and the three middle names will have close family lineage and meaning for the couple. I use Frances/Francis (not sure of which spelling as I have seen both mentioned for either gender) in the middle for either: to honor Diana's middle name for a girl and a long line of Frances/-is on Catherine's father's side for a boy.
Thus, my guesses...
Mary Alexandra Frances Elizabeth
George Francis Arthur Charles
I find myself wondering how boxed in they are.
On the one hand, many people argue that they'll only use a name that's been used for a reigning monarch before, but isn't currently in use in the family. Once you toss out Richard and John, because they are regarded as bad karma, that leaves George and Victoria.
On the other hand, they could go with a traditional Scottish monarch's name, which broadens the field to include Alexander, Robert, Malcolm etc. They could also go with names that have been used in the royal family before, albeit not for monarchs, which gives them options like Charlotte or Frederick.
As an added wrinkle, they are millennials, and William's cousin, the only one of the Queen's grandchildren to have kids, has named his daughters Savannah and Isla, which are just names that are popular in the UK now. My bet is that William and Kate won't go quite this contemporary, but they may not feel obligated to just pick from the batch that's been used before.
A further complication is that the kid, upon assuming the throne fifty years from now, can take a regnal name that can be whatever they want.
Peter and Autumn Phillips (the Queen's grandson and granddaughter-in-law) got away with naming their daughters Savannah and Isla, because however harsh it might sound, they are "commoners".
Peter might be the Queen's grandson, and he may be in line to the throne, but he is not technically royalty.
His father was not 'blue blooded', and royal titles are weighed very much in paternal lines, and as such Peter (and his sister Zara) have no right to a title. The Queen did offer to issue a decree giving Peter a title, but Princess Anne refused (as she did when the Queen repeated the offer after Zara was born), wanting her children to have normal lives and not been weighed down by royal duty/protocol.
Unless there is a great royal tragedy that wipes out everyone before them in the line of succession (!), Peter's daughters will never ascend to the throne, so their names are inconsequential.
William and Catherine's baby will one day be the heir to the throne, and as such, William and Catherine will face greater constraints when choosing a name. The Queen will have to approve the name, that's well documented.
However much we might all dream of them being bold, and stepping away from the names used before, the likelihood is that simply won't happen.