"Як мене звати?"
Переклад:What is my name?
I am sorry, but I don't see your point at all. Are you trying to prove that звати exists in Ukrainian? Everybody knows that. Are you trying to show what звати means in Ukrainian? I guess that's not a big secret too. That звати is "call" in English? Yep, that's true.
"Як мене звати?" idiomatically means "What is my name?". I don't think that one would use "How do you call me?" to mean that. "How do you call me?" would rather be translated to Ukranian as "Як ви мене називаєте?" (if they call you something other than your name and you wanna know what exactly)