"Vous vous appelez Laura" means:

Question

Surely
 Your name is Laura
You call yourself Laura
means the same thing

Accepted Answer

Vous vous appelez Laura in French has the same function as "Your name is Laura" in English. Therefore that's the proper translation. The fact that, literally, it translates to "you call yourself Laura" in English is not really important and only confuses the issue.

Answer

Bonjour à tous,

To be called [something] = my name is [something] -> s'appeler [quelque chose]
To call yourself [something] = to go by the name of [something] -> se faire appeler [quelque chose]

This is an excellent explanation: Referring to one's name
I hope this is helpful.
Bonne journée !

Answer

In English, if you want to learn someone's name, you don't ask, "What do you call yourself?". However, in French you DO say, "Comment vous vous appelez?"

Answer

I agree with Philip.  If you intend for the only answer to be ‘Your name is Laura’ then do not include ‘You call yourself Laura’ in the answer selection.  Both answers are correct.

Answer

I came here for the same reason. Having read the lesson I understand why
 it's not considered the correct translation, but to mark "you call 
yourself Laura" a wrong quiz answer is confusing. It wouldbe better if you just removed it 
as an answer choice completely.