I've seen a lot of different translations like, "компьютер саенс" and "Компьютерные науки" and I was wondering which one is correct
"Информатика" is the closest you can get. In the Russian-language wiki article on "Computer Science" you can find more about the history of this term in different languages. In the same article you can find also term "наука о вычислительной технике" which is used but very, very limited.
The strange thing about "информатика" that it de-facto getting slightly outdated (like it happened with "кибернетика" earlier) but there's no decent word or phrase we can use and claim to be modern. Nobody says "компьютер сайенс" though, that's for sure. For the lack of a better term one can use just computer science.
As a college/uni subject it's "информатика". Same as in French (l'informatique).
By no means компьютер саенс.