Generic drug name for crestor?

What is the generic name for Crestor?

Crestor is the brand name for rosuvastatin [1].

Does “generic Crestor” always mean the same drug?

Yes. Any “generic Crestor” product will be rosuvastatin (typically listed by dose strength), because rosuvastatin is the active ingredient under the Crestor brand [1].

Sources:
[1] https://www.drugs.com/brand/crestor.html