In languages verbs are usually followed by direct objects (accusative case).

For example: I(subject) call him(direct object, accusative) = я зову его.

When we say names in Russian , we do this literally like this : (they) call me Rachel= (они) меня зовут Rachel. We omit (они) in this case, but the conjugation is like for 3rd person plural. Such usage is kind of passive construction. меня  = direct object, accusative.

All pronouns in accusative are : меня, тебя, его, её, нас, вас, их

To express possesion we say literally: at me there is something=  у меня есть что-то (means I have something).

After propositions we use specific cases,e.g. after prepostion "у" we always use Genetive case, which is for pronouns identical to accusative one.

However if a vowel comes after a preposition, we add "н" to the beginning of a pronoun.

For example: He has something. We don't say "у его есть что-то", but "у Него есть что-то".

Example From your sentences "он есть дети" is incorrect, we use "у него есть дети" instead.

У меня/у тебя/у него/у неё /у нас/у вас /у них/ есть семья.

меня/тебя/его/её/нас/вас/их  зовут ...

there are 3 mistakes in your exercise.