"My name is Vanya."
Translation:Меня зовут Ваня.
Because «у» is the preposition that indicates either possessor (when used with living beings), or being close to something (when used with inanimate objects).
So, «У меня зовут» is 'at my [possession/place] is named/called'. This sentence is incomplete: it doesn't specify who is named/called at your place/possession.
[ Вопрос: Как ваше зовут?
[ Вопрос: Как ваше имя?
[ Ответ: Меня зовут Ваня.
[ Вопрос: Как ваше | Фамилия, имя, отчество ]
[ Фамилия, имя, отчество · http://context.reverso.net/перевод/русский-английский/Фамилия+имя+отчество ]
[ Как ваше имя · http://context.reverso.net/русский-английский/как+ваше+имя ]
[ Мое имя · http://context.reverso.net/перевод/русский-английский/мое+имя ]
What I have figured out is that Меня means "me" and зовут is the conjugation for the third person of the verb to "to call", so the sentence stands for "they call me Vanya"
While this works as a literal translation (somehow), sentences with 3rd person plural verb and no subject have an idiomatic meaning in Russian: they're called indefinite-personal sentences and they are used when the actual subject of the sentence is unknown or unimportant. So, this sentence doesn't mean that the subject is plural ('they'), this subject just means that I'm called Vanya and it's not important who calls me like this.
Indefinite-personal sentences (неопределённо-ли́чные предложе́ния) are often translated with the English passive verbs. Sometimes, they can be translated with 'they' (e.g. «говорят» = 'they say', when relaying rumours), but usually passive works better.
But in the case of «меня зовут», "my name is" is just a more idiomatic English translation.
Because it means "my first name is Vanya". I know this lesson is trying to teach the accusative form, but I believe mine is a valid translation.
It does matter which word you use. Моя is a form of the word that means "my" and does not make any sense in this sentence (which, put literally would be something like "(They) call me Vanya").
The verb takes a direct object. If you want to say "Моя . . . Ваня", then "Моя имя - Ваня" is an option: "My name (is) Vanya".
It is моё имя :).
Имя is neuter. Russian has got 10 such nouns—nouns, of which a beginner only needs «имя» name and «время» time (OK, maybe «пламя» flame and «племя» tribe if you are a bit more advanced).