"Меня зовут Ваня."

Translation: My name is Vanya.

[langjd]

Do Russians actually use the diminutive forms of their names when introducing themselves?

[amaratea]

Yes, in a proper situation (when it's not too formal and official, they are relatively young, it's a friendly meeting etc)

[Theron126]

Kids on a playground was what this sentence suggested to me, I guess that would be an appropriate interpretation?

[amaratea]

Kids on the playground for sure, what I meant to say is that it is not only for children.

[langjd]

Thanks!

[alback-isback]

"they call me Vanya " should be accepted as well

[KVinayak1]

Does it mean "I am called vanya" ?

[MishaFromMayo]

Yes. Literally, it's "They call me Vanya."

[PetarKresimir]

So, i would use this to introduce myself to somebody in a friendly manor or is ot still considered childish?

[amaratea]

It's not childish. Many people usually go by diminutive forms in everyday life, myself included.

[stijnboy01]

Why is it Меня and not another form of "I"?

[Berniebud]

The literal translation for this sentence is "Me they call Vanya" "Меня" being the accusative form here.

[sarahmv04]

Isn't the они form of the verb to call звонят? Why is зовут used?

[Randonneur3]

звать -> они́ зову́т
звони́ть -> они́ звоня́т