。
I do know his name, you know.
Literal
His name [topic-は] properly know-am [emphasis-よ].
Subject is omitted (the speaker). ちゃんと ('properly, precisely, for real') is a workhorse adverb of casual Japanese — asserts that the action is being done correctly or seriously. 知ってる is the casual contraction of 知っている. The よ claims it as known information against implicit doubt.