In the 19th century the name of the valley in Germany was spelled "Neanderthal", and now it seems to be "Neandertal", with exactly the same pronunciation. But as far as I knew before tonight, the name of the extinct species was always "Neanderthal" when writing in English. But now I find this article. Have Anglophone scientists now finally adopted the modern spelling? And in English, this might change the pronunciation. Is that happening too? What's the story behind all this?
According to the Grammarist both spellings are correct but the original one "Neanderthal" still remains the more common:
Neanderthal is the more common spelling of the noun denoting the species of robust humanlike creatures that went extinct around 30,000 years ago. Neandertal is preferred by a few scientific publications.
Neanderthal, the original spelling, was derived from the German valley where Neanderthal fossils were first discovered in the 19th century. In 1901, however, the German name of the valley was officially changed to Neandertal. Some scientists and scientific publications have extended the change to the name of the species. Most have not.
Nonscientific publications show a similar trend. Neanderthal is preferred, but Neandertal appears about a quarter of the time Neither spelling is inherently correct or incorrect, but some scientists do have strong feelings on the matter. If you’re writing for a professor, find out what he or she prefers.
Also Ngram shows a clear preference in usage for Neanderthal.