The variation in spelling occurs in Russian transliterations because of a linguistic trait common in Slavic languages (and others) called final consonant devoicing. Rachmaninoff's (I use this spelling) name may end with a letter that directly transliterates to V in the Cyrillic alphabet, but V is devoiced at the end of a word to F. Similarly, Z devoices to S and B devoices to P at the end of Russian words, to name other examples. It is interesting to note that with many other Russian composers and performers, the transliteration of their name is directly done, as opposed to taking into account final consonant devoicing, and some examples are Nikolai Petrov, Mily Balakirev, Edison Denisov, and many, many others. Rachmaninoff perhaps used this spelling because he knew English. And, if you are already confused, this only is the tip of the iceberg as far as other transliteration anomalies. There are probably thousands of ways to validly spell these Russian composers/performer's names.