Go with whatever Wikipedia uses.
Sergei Rachmaninoff instead of Rachmaninov, or Сергей Васильевич Рахманинов
In the UK they prefer "Rachmaninov." Just look at innumerable British CD covers and reviews in Gramophone & BBC Music. But HE preferred "Rachmaninoff." That is, he based his preferred Roman-letter spelling on a French rather than a German model. He's buried in New York state (Kensico Cemetery, Valhalla, Westchester Co., NY) as "Sergei Rachmaninoff." His record label, RCA Victor, always spelled it "Rachmaninoff." It's fair to point out that a music scholar I know who speaks Russian prefers "Rakhmaninov."