In Russian sources that I can find, it goes like this:

1954 - ПП-1 (prototype / proof of concept)

1955 - ПП-2 (for Strela-1)

1955 - ПП БЭСМ (for BESM)

Followed by more versions for various new mainframes that appeared, named by suffixing "ПП" with the name of the hardware - e.g. there were distinct versions of ПП for Strela-3, Strela-4, and Strela-7.

The abbreviation itself stands for "программирующая программа", "a program that programs". So it sounds like it was originally a name of the specific prototype, but then became a generic term for any kind of compiler for a short while (later replaced by "translator", probably under the influence of FORTRAN and ALGOL).

For some reason they don't mention ukrainian https://en.wikipedia.org/wiki/Address_programming_language which, according to some sources, was used to program soviet ballistic missiles.