So the word has not changed - the spelling is just catching up with the pronunciation.
It was in 1924 that the Germans completely restructured their written language to match pronunciation. "Neanderthal" has always been pronounced "Neandertal". It has never been pronounced (at least not properly) with the soft "th" sound, as that sound does not exist in the German Language.
But, the above poster thought it was a pronunciation shift, so I pointed out, it wasn't.
In fact, it was the LAST surviving silent letter in German. And now it is gone.