I still predict they will go with something that is in style right now, not a name from the royal family.
I think you can look at the current top 10 in Australia and Denmark and probably make a good educated guess about what will be the names.
Denmark's top 10 names for 2009 for boys: Mikkel, Lucas, William, Emil, Noah, Victor, Magnus, Oliver, Frederik, Mathias.
For girls: Freja, Ida, Emma, Lærke, Caroline, Anna, Isabella, Sofie, Mathilde, Sara.
Most popular names in the Australian state of Tasmania for boys in 2009: Oliver, Lucas, William, Riley, Thomas, Lachlan, Noah, Samuel, Harry, Jack.
For girls: Charlotte, Ruby, Ella, Matilda, Grace, Amelia, Lucy, Chloe, Isabella, Sophie.
Overlapping names on both lists: Lucas, William, Oliver, Noah, for boys; Matilda/Mathilde, Sophie/Sofie, Isabella (which is taken already and isn't in the running.)
Rule out also obviously unroyal or too obviously un-Danish sounding names like Riley, Lachlan, Harry, Jack, and probably Noah; Lærke and Ruby. Others on both lists are melodious to the ear and could sound right followed by Prince or Princess.
When she picked one of the most popular names in the English speaking world for her daughter, I think Mary showed that her taste tends more towards the contemporary and I would guess she'll lean that way in naming the twins.