EDIT. As Dirk pointed, when you cite a paper (written in Latin font) you always
write the author's name exactly as it is written in the paper.

When you cite a paper which is written in some other alphabet,
the following are two reasonable approaches to this that I know: 1. To follow Mathscinet.
2. If an author ever wrote a paper using Latin font, write his name as he did himself.

Of course these approaches give the same result in most cases, but the second is especially important when you cite old authors who are not in Mathscinet,
for example, Chebyshev. (There was a nice joke in one combinatorics book: Problem. How many ways are there to spell Tschebyschev in English?).

It happens that the same author (or the translator) wrote his name with different spellings in different papers in English. In this case, when you cite his paper, just follow the spelling in the paper that you cite. 

EDIT. Here is a little example which shows how good the Mathscinet author database is. American mathematician D. F. Shea once published a paper in a Ukrainian journal, in Russian, and this paper was later translated to English. The translator of the paper transliterated his name from Russian as "Shia". Nevertheless Mathscinet determined his identity correctly.

EDIT2. There is a remarkable book on the subject of Chebysheff's names (first and last), and many other related important subjects:

The Thread: A Mathematical Yarn Paperback 
by Philip J. Davis , 1989.

Strongly recommended.
However, the author is not a native Russian speaker, so he does not discuss such advanced topics as the one in @Fedor Petrov comment.