Vous vous appelez

The two vous fulfill two different grammatical functions: the first one is the subject and the second one the object of the sentence. Literally, comment vous vous appelez translates to how do you call yourself. The first vous is "you" and the second one "yourself".

If you use first person singular, the difference becomes apparent because the words for "I" (je) and "myself" (me) are different in French: je m'apppelle.