No, it's Mauretania only once, because that was the Roman name. English chose to use a slightly different name for the country, some other languages didn't.
Moor derives from mauri. To quote this site, "from Greek Mauros, perhaps a native name, or else cognate with mauros "black" (but this adjective only appears in late Greek and may as well be from the people's name as the reverse)."
I am Greek. I can definitely say so
Mauros=black
so its not country of the moors but country of the blacks!