"Proč chceš vědět, jak se jmenuje?"

Translation: Why do you want to know what her name is?

[Lars1o2]

Why should this be 'her' name and not 'his'?

[ValaCZE]

There can be both his, and her. I will add it.

[Jenda-48]

What is your name. Jak se jmenujete. Ok
What is she name. Jak se jmenuje. Ok
But here "Why do you want to know what is her name?" is wrong. Please, why?

[BoneheadBass]

Your suggested answer is a non-standard word order in English. If you used it, you would be understood, but if would sound odd to native speakers.

[VladaFu]

The second clause is not a question, it is a reported question, it has the normal word order.

[jenda48]

Díky

[venik212]

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.