How would you translate
privacy into Russian?
May I have some privacy?
I care about my privacy.
I think we have a case of a concept not really present in the Russian linguistic world image. One can speculate if the privacy has not really been valued until recently, but that's beyond the point.
AFIK, there is no good translation. Lately, I have been encountering the word
приватность, but I don't think it is standard.
If you have to translate it, you have to reword it taking the context into account. For example, you might translate
Can you give us some privacy? as
Не могли бы вы оставить нас одних? Or you might translate
I value my privacy. as
Я не люблю когда лезут в мои дела.
Additionally, you should read this article:
How would you translate privacy into Russian?
"Приватность". The IT sphere is the first in line of borrowing of words from another languages.