Yep. The question is deeper than nomenclature.
Could H. Neanderthalensis mate with H. Sapiens and produce viable and fertile offspring?
Given that there are varying degrees Neanderthal DNA in some human populations, I’d say yes, as repugnant as the thought may be, interbreeding was possible.
Why would it be repugnant? Maybe some of the Neanderthals were fine people. Who is to say that one of them could not have learned to do a Sudoku puzzle as well as anyone alive today? Or become a chess master? Certainly none of them was as evil as some members of our species (Stalin, Hitler, Che Guevara, Pol Pot, Saddam Hussein).