Слушай здесь http://uk.forvo.com/search/зовут/

"Zavut" is the right way to pronounce it. Even if you speak slowly.

In russian language when the letter O is out of the accent - it is pronouncing A. (kak vas zAvut) but (zOv) milk - молоко (mAlAko)

Read about vowel reduction. In most (minor) variations of modrn Russian O and A are indistinguishable in unstressed syllables (they become an "uh"-like sound), and so are И and Е (they become an i-like sound). By the way, the true rule is a bit more complicated and there are very few exception (около and возле have an audible first O, and in some foreign words like "радио" you also hear "О"). A person will only pronounce "зовут" with O if they are reading out how you should spell the word or if their accent keeps vowels in stressed and unstressed syllable different (eg. Ukranian or some southern Russian accents) Try Forvo if all you need is pronunciation of certain words. :)

зовут => завУт