"What is your name?"
Translation:Як тебе звати?
OK, so the simple answer is:
Як вас звати? = How are you to be called? - literally.
In English, you can ask, "What are you to be called," but that's unnatural. In Ukrainian, що means "what," but its case would decline in this sentence. Чим вас звати? is very bad Ukrainian anyway.
Що can't be an attribute of a noun ('a name' in this case). It's a question word that means "What" only in phrases like "What is it?", "What did he say?" or "I know what I'm doing". You should look here at the pair "what name" which means "яке ім'я". And the whole cliche "What is your name?" corresponds to "Як тебе звуть?" or "Як (or more seldom яке) твоє ім'я?"