"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.