It has been said that protocol dictates that if it were to be a girl she should be named Margrethe... I disagree

. Not because I don't think that Margrethe is an ugly name, quite the opposite, but because simply having two queens that have had the name Margrethe doesn't mean that it carries a real predecent that has to be followed. (Though people may see it differently, and I thought Princess Ingrid of Norway would be named Margrete because of the predecent... *shrugs*)
Especially since the two Margrethes were so far apart. When Queen Margrethe was named it was not intended that she was to be queen. At that time any brother she would have had would predecede her, as did her uncle and her male cousins.
If Frederik & Mary should get a daughter first, then a son, as far as I understand the danish constitution, the son would inherit the throne. (There are talk of changing this, but it seems like a lot of politicians have a "wait and see what happens" attitude.)
Therefore the predecent is that the girl should have one of her mother's names, as Queen Margrethe, Princess Benedikte and Queen Anne Marie are all called Ingrid. Elizabeth would be a pretty name on a girl. Not very Danish, perhaps, but it would be nice to let her have some connection to her mother's original heritage.
It's four names the Danish royals have, right?
Some suggestions from me.
Female:
Elizabeth
Dagmar (hey, it means Glory of the Danes, not a bad thing.)
Kirsten - a form of Christian.
Margrethe - I do like it.
Gu?run - a faroese name.
Henrietta - Mary's mother's name, but at the same time also a nod to Prince Henrik.
Male:
Christian
Frederik
Valdemar
Gorm
Harald
Knud
These things are impossible to guess. Though the guessing gets easier with a baby actually on the way... or actually there..