I'm not entirely sure that the way Rahmaninov (see further) signed his own
name in English should be considered definitive.  To represent words from
languages which use different character sets (say, Cyrillic and Latin, used
respectively by the Russian and by the English languages) it is necessary
to adopt a transliteration rule.  Note that transliteration doesn't pay
attention to the pronountiation of the word once transliterated (since that
would vary from language to language); what it does assure is that the word
could come and go from one character-set to another any number of times
without corruption.

There is an international standard for the transliteration of Cyrillic
into Latin characters; it is published by the International Standards
Organization as ISO 9:1985 and is always used when rigor is necessary,
as in scientific works.  According to that norm, the name we're talking
about would be written "Sergej Rahmaninov".

Using the pronounciation criteria lends to different results.  Just to
illustrate the point, another distinguished Russian artist is referred to
as

- Shostakovich in English;
- Chostakovich in French;
- Schostakowitch in German.

The standard transliteration would be "Dmitrij Sostakovic" (but note that,
according to the Standard, both the first "S" and the "c" would have to be
marked with a diacritic sign that resembles and inverted circumflex which
is quite usual in Czech).  An earlier composer quite influential on both
above was "Caikovskij" (with an inverted circumflex over the "C").

p.s. For more information on the ISO standard, see
http://www.iso.ch/cate/d3589.html

Paulo J.P-Braga