Why is it:
Как тебя зовут? = How's your name?
and not:
Что тебя зовут? = What's your name?
Why is it:
Как тебя зовут? = How's your name?
and not:
Что тебя зовут? = What's your name?
Как тебя зовут literally means "how do they call you?".
It's an idiomatic way of asking for someone's name, and it actually works this way in a lot of languages other than Russian: Come ti chiami?; Wie heissen Sie? etc. Even in English, "they call me John" is a valid, if pretentious way of introducing yourself.
When you're asking for someone's last name or patronymic, your would use Как ваша фамилия? or Как ваше отчество?, which are closer to the English way of putting it.
However, they also use как instead of что. Literally, you'd be asking "How's your last name?". This is because Russian tries to avoid syntactic ambiguity in cases where что could be both a subject and an object.
When you ask something like Кто твой папа? "Who's your dad?", there are two possible answers: Он мой папа "He's my dad" or Мой папа плотник "My dad's a carpenter". In the first case, the answer to кто is the subject; in the second, it's an object.
Russian, for some reason, avoids that kind of ambiguity for the word что. If you want to ask "What do you call a mouse?", you have to think first which blank in the phrase "you call <a thing> <a name>" you want the answer to fill.
If you're looking for the thing, i.e. an answer in the form of "you call a computer device a mouse", then you'd phrase the question as Что такое мышь?.
If you're looking for the name, i.e. "you call a mouse Whiskers", then you'd phrase it as Как назвать мышь?
"Как тебя зовут?" literally translates to "How are you called (by others)?".
"Что тебя зовут" is ungrammatical. You could say "Чем тебя зовут", but that's just unidiomatic and sounds weird outside of certain specific contexts.
English and Russian work differently, and there are a lot of cases where you can't translate phrases word for word.
"What's your name?" would literally be more along the lines of "Каково твоё имя?", which is actually correct, but sounds like something medieval.