The problem to me is more that 저는 would imply some higher formality in verb than what is done here.
Otherwise it would be ok I think. You're not talking about the teacher here, you're talking about yourself not knowing something. I might be wrong though.
Would 선생님의 be correct if it was used in this sentence? In addition, could «I do not know the name of my teacher» be a valid translation? It was not accepted, so I am wondering if, in that translation, a subtle part of the original sentence's meaning was lost.