I think they will steer clear of Alexander/Alexandra because of the Countess...the most likely nickname for those names is "Alex" and it might be too much and too fresh in some peoples minds...They might also steer clear of Jorgen for the same reason (Martin and Alexandra Jorgensen?)...
For girls I have lots of ideas, but since four names seems to be the limit, it will be hard to choose the *TOP 4*
Henrietta - Mary's mother
Olympia - perhaps to signify their meeting place (Sydney 2000 Olympics)
Matilda - vague Australian reference, Waltzing Matilda, and it is very European royalty anyway
Maria - another version of Mary and also the Russian name of Empress Federovna (?)
Dagmar - the Empress's Danish name and rumours started at her reburial
Xenia - just an interesting royal name with connections to the Empress, her daughter I think?
Arabella - a Scottish queen's name that sounds very regal and probably equally at home in Denmark too...the whimsy name, if you will
Margrethe - Frederik's mother who will most likely be suitably honoured...
Ingrid - Frederik's favourite grandmother...
Ok that is 9 names...now to make a four name combination that pleases everybody!!!
Princess Arabella Dagmar Henrietta Marie
Princess Xenia Dagmar Henrietta Margrethe
Princess Henrietta Dagmar Margrethe Ingrid
Princess Matilda Margrethe Henrietta Ingrid
Princess Matilda Olympia Margrethe Ingrid
Princess Matilda Olympia Ingrid Henrietta
Good luck to them...naming a boy sounds a lot easier
Prince Harald Abel Vilhelm Frederik
Harald - because it is historical and has a cool nickname of *Harry*
Abel - vague Tasmania reference...Abel Tasman, who discovered the island and it is also a royal name
Vilhelm - Danish form of William and it has royal connections
Frederik - the child's fathers name
I just had to put in my last two cents because the baby is due pretty soon...but we have to wait until July/August anyway for its christening :(