Oy! But his dad was sort of Russian (of Belorussian Jewish ancestry and growing up in a country with Russian the official language). The native spelling was not in Latin characters so there was a bit of freedom of how to transliterate the name: Фейнман.

Had he moved to the USA in the middle of the century, the standard of the transliteration then was to convert the "й" character to "j" so he could have been Fejnman.

It is also possible that the original name was indeed Feinman in Yiddish with "ei" read as in German (the long i), which would explain how it became Фейнман in the first place (transliteration from German Yiddish by a simple substitution based on the spelling while distorting the phonetics). Some Russian Jewish names appear to have gone through a similar process. This is speculation, however; I have not done any research on the origin of the Feynman's family name.