Translation:He did not even want to know my name.
This is a perpetual problem with Duolingo; they insist upon their English grammatical translations for their Italian sentences when there may be several ways in English to say what their Italian is expressing. I literal translation of the above would be, "He did not want to know not even my name." Clearly incorrect as an English translation because of the double negative. But there is nothing wrong with leaving the "even" in that position. We are all learning that the program is really not for teaching language, but for translating them, an agenda that is separate and apart from the uses of laypeople. Still, it could evolve quite a bit as a teaching tool of there were incentive for it. I hope it does.
five years late, if you mean at the beginning of a clause or sentence (nemmeno se mi dai un milione...) yes; but the meaning is a little different. it usually means 'not even...' as in this is insufficient. in this sentence it means 'nothing' he wanted to know nothing.