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.
A crown prince is set to inherit the crown. He may have younger brothers, and they would just be princes.
Once our current crown prince becomes king, his eldest will become Norway's crown princess.