The short answer to your question is that major style guides offer detailed and somewhat varied guidelines for handling the personal names of people from other countries and languages. Because the advice tends to be extensive, I'll limit myself to discussing the handling of Russian names recommended by three prominent U.S. style guides: MLA Style Manual, Chicago Manual of Style, and New York Times Manual of Style and Usage.
From Joseph Gibaldi, MLA Style Manual and Guide to Scholarly Publishing, Second Edition (1998):
3.6.9 Russian Names
Russian names have three parts: prename, patronymic, and surname (Anton Pavlovich Chekhov). Prenames of Russians should be transliterated according to the appropriate system rather than given in their English equivalents (Ivan, not John). The only exception is the prename of a Russian ruler used alone (without the patronymic); in this case, use the English equivalent (Michael I, but Mikhail Pavlovich).
The form of patronymics in Russian varies by sex, as the form of surnames often does. For example, Aleksandr Sergeevich Pushkin was the husband of Natalia Nikolaevna Pushkina. The treatment of such names in an English text depends on the audience, on the predominance of masculine or feminine names in the text, and particularly on whether the text uses names without prenames. In general, the feminine forms should be used for the feminine names and the masculine forms for the masculine names. On occasion, however, especially in a casual reference to Russians in a work not on Russian studies, some modifications may be acceptable. Scholars not familiar with Russian names must exercise care in balancing accuracy with clarity.
From Chicago Manual of Style, Fifteenth Edition (2003):
8.15 Russian names. Russian family names, as well as middle names (patronymics), sometimes take different endings for male and female members of the family. For example, Lenin's real name was Vladimir Ilyich Ulyanov; his sister was Maria Ilyinichna Ulyanova. In text often only the given name and the patronymic are used; in the index the name should be listed under the family name, whether or not this appears in the text.
From Allan Siegal & William Connolly, The New York Times Manual of Style and Usage (1999):
Russian names. Names that have become well known in English should keep their familiar forms: Peter the Great, not Pyotr; Tchaikovsky, not Chaikovsky; Khrushchev, not Khrushchyov; Rachmaninoff, not Rahkmaninov. (Another exception: czar, not tsar.)
Women's names in Slavic languages have feminine endings. Use such an ending when a woman has a reputation under her own name: the ballerina Maya Plisetskaya, for example, not Plisetsky. But Naina Yeltsin (not Yeltsina), the wife of President Boris N. Yeltsin.
As this last excerpt suggests, New York Times style is to render patronymics as one-letter abbreviations (Boris N. Yeltsin, instead of Boris Nikolayevich Yeltsin), whereas Chicago takes a much less prescriptive position, merely noting that "In text often only the given name and the patronymic are used." For its part, MLA advises carefully tailoring the naming style to the type and tendency of the work being written, and carefully "balancing accuracy with clarity."
Each style manual offers similarly detailed (and by no means unanimous) advice for Japanese names, Spanish names, and others. Your best bet is to determine which (if any) style guide the publisher or organization you are writing for prefers, and use its style. If you're free to choose a style strictly on the basis of personal preference, do so—but then follow it consistently.