@keinemeinung: to my native-speaker ear, “I’m called Ivan” is completely natural, and equivalent to “My name is Ivan” as a standard way to introduce oneself. (As opposed to e.g. “They call me Ivan” which is indeed less standard, as other comments say, and so makes sense to reject.)
"I'm called Ivan" was rejected 31 July 2018.
To me as a native speaker of American English, "I'm called Ivan" is effectively synonymous with "My name is Ivan;" much as "I couldn't say" is effectively synonymous with "I don't know." While these both can sometimes be parsed down to their literal meanings ("My name is Theosiphus, but among my Russian speaking friends, I'm called Ivan," "Without breaking my promise of confidentiality, I couldn't say"), mostly they are just exactly equivalent phrases.
The American classic novel 'Moby Dick' famously uses "Call me Ishmael" as its opening line. This leaves the reader with the impression that the narrator is named "Ishmael," and it is only as the events of the novel develop that we realize that "Ishmael" is probably a pseudonym.
"They call me Ivan" is indeed very different from "Call me Ivan," and is not generally used when introducing oneself. A case-in-point example of when its use is in the 1967 film 'In the Heat of the Night' (also an American classic). Gillespie, a bigoted White sheriff in the 1960's-era American south, has been demeaning an African-American man named "Virgil Tibbs" by using his first name repeatedly and without invitation.
But even this isn't demeaning enough for Gillespie, and he demands: "'Virgil'? That's a funny name for a n----r boy come from Philadelphia. What do they call you up there?"
Tibbs responds: "They call me MISTER Tibbs!"
"Call me Ivan" is about what your name (or chosen moniker) is. "They call me Ivan" is about what others call you with or without respect to what your name is.
Well, it can, but it's not what we mean.
"They call me Ivan" = "Они зовут меня Иван", and it doesn't say if Иван is my real name, just them calling me like this. See?
Also, we can say "Моё имя Иван" = "My name is Ivan", but it sounds strange and unnatural in everyday speech, so better stick with what Duo has.
Because меня is the accusative/genitive form of я, and equivalent (roughly!) to "me" in English. меня is the object of the verb зовут.
In English, if this was translated literally, it would mean 'they call me Ivan'. Saying я зовут Иван would be the equivalent of saying 'they call I Ivan'.
Edit: okay I realised I'm tired and I slightly misread your query; in Russian, what we actually say (versus how one translates it) is not actually "my name is", it's "they call me".
If you were giving someone your name to write down, say you were saying my surname is, my forename is, then you would indeed use a form of the possessive pronoun my/мой. However, it's just not how it's said in Russian :)
"Yes, I am called Ivan" is the answer most of us are looking for, and what most of the comments here are about. I don't get why this wouldn't be added as a correct answer either... It is completely natural in English, and the most apt translation for this sentence. I can't believe this has been an issue for over two years!