Translation:Do you know what the crown prince's name is?
"Do you know the name of the crown prince?" Actually, this would be a better translation to proper English. Ending a sentence, even a question, with a preposition is incorrect, despite it's common, modern use. Duolingo generally suggests common usage rather than the legal, proper form.
But there is no preposition in the original sentence. 'Is' is not a preposition. There's absolutely nothing wrong with saying "Do you know what the crown prince's name is?"
Ending sentences with a preposition is not really wrong or improper, either; it was basically a (very successful) linguistic crusade perpetrated several centuries ago that a lot of people listened to and believed. But since there's no actual preposition here, I'm not going to get into that further. ;-)