Translation:Why do you want to know what her name is?
IMHO Jenda is right, and Vlada said, correctly, that the second clause is NOT a question here, but rather the thing that you want to know. Just think: Why do you want to know her name? Or: Why do you want to know how to speak Czech? The question in the first clause does not necessarily change the word order in the second clause, even if in some instances some native speakers might find it unnatural.