US equivalents of Russian academic titles
From how it should work, the situation is like this:

Kandidat nauk (кандидат наук) is a PhD holder. Not a PhD candidate, but a done PhD.
Doktor nauk (доктор наук) is something not really common in the US system. It's the higher doctorate in the UK or a habilitation in a European system.

Now what you get recognized depends on the local authorities, but ideally that should be it.
Bonus: the typical position names in ex-Soviet system are junior and senior research staff (младший научный сотрудник, старший научный сотрудник). Typically, you have the former when you are doing your PhD and the latter when you are a postdoc/tenure track researcher.