Quote Originally Posted by Platinum
To clarify my question, I was trying to ask my friend the first name of his father.
"Как зовут твоего отца?", though perfectly normal and usual, is, in a sense, ambiguous. You will get either the first name or "имя-отчество". The latter is more likely in this case.
"Как имя твоего отца?" will almost certainly get you the first name.