"I do not know your name."
Translation:Non conosco il tuo nome.
You could say, "Io non ti conosco.", but "Non conosco il tuo nome." is not correct. "Non so il tuo nome." is correct.
"Non conosco il tuo nome." can only be correct if you mean something like you have a very strange name and I'm not familiar with it, but that is very different from says you just don't happen to know someone's name.
that's how I translated it and it marked it correct, so I guess it's fine...
Can you use the 'familiar' tuo if you are so little acquainted that do not know their name?
Well, depending on the context it might be possible; for instance in a work environment where 'tu' is favored, like mine, you might end up using a polite wording such as this to ask a colleague's name. The formal context is more likely though.
What's the difference between "so" and "conosco"? "Non consco il tuo nome" sounds rather like "I don't recognize/I'm not familiar with your name."
You should always use some kind of article before possessive words like «tuo» except when the noun following is it a singular family member.