Originally Posted by König

Not a bad advise; however, there might be some unexpected consequences. Russian names are written in Cyrillic script, and what exists in external passports are just their transliterated versions. The rules for transliteration use phonetics, so for instance, letter "ж" is transliterated as "zh". For instance, if somebody with the name John Cortney becomes Russian citizen, his name in Russian will be Джон Кортни. His transliterated name in external Russian passport may well be Dzhon Kortni The same situation would apply to those dual Russian-American citizens who want to change their Russian names to reflect American names.

I do not know if a person can ask for an exception from transliteration rules in Russia. Even if so, it will have to be done with every external passport renewal application.