I think as the couple named their daughter Isabella which is not a Danish name in first place, I do not think they will go for traditional Danish names at all. And if they did, probably only in relation to the family tree. I'm not fond of modern names for royal children, but I believe they will choose a modern one. Speculation is more or less senseless, we will see the result soon enough.
There are a number of Isabellas in the family tree, and not all married into it. The name is not as rare as some made it out to seem.
Eric V had a daughter Isabella
John of Denmark had a daughter Isabella who married the elector of Brandenberg (Her brother Christian II's wife Isabella is who modern day Princess Isabella is speculated to be named for)
Frederick I had a daughter Isabella
Frederick II had daughter Isabella who married the Duke of Brandenberg
Christian IV had a daughter Sophia Isabella with his wife Christina Munc, and a daughter Isabella with his wife Anna-Catharine of Brandenberg
So Mary and Fred's daughter is at least the seventh Danish princess born with the name Isabella.
I really like the Anna-something. It would be an honor to Anne-Marie but is also very common in the Danish tree, and Prince Henri also had a sister Anne-Marie who died young. The second part could be a name they love but which has been used recently like Sophia, to give it a new form.
Anna-Caroline
Anna-Sophia
Anna-Theresa (Theresa a siter of Henri)
Anna-Catherine (also a sister of Henri)
Anna-Charlotte
Anna-Christina (perhaps not due to closeness to Christian)
Anna-Helene
I really like Anna-Catherine
Princess Anna-Catherine Benedikte Mary Patricia: the queen's sisters, Henri's sister, and Mary and her sister
And Abel I recomended due to the link to Tasmania but perhaps not. Joachim was slightly less traditional for a second son, (seems to be the father in law of Christian IV)
Prince George Friedrick Peter Canut- George from the family tree, Friedrick for Fred, Peter for Mary's family, Canut for Margrethe's Uncle
So
Anna-Catherine Benedikte Mary Patricia
George Friedrick Peter Canut