Relatively common, my wife does it all the time. When she was on a GC, travel was booked using her Russian passport, and the GC was used for entering the US. Now with a US passport, travel is booked with that name and she leaves and re-enters the US with that passport only using the Russian passport for entering and leaving Russia, and booking any domestic Russian flights. She always keeps a copy of our marriage certificate with her, but in 10+ years, not a single person in any country has asked to see it.
I do agree with @OldUser, if you can change the name on the German passport relatively easily, I would do that. In Russia it is a real pain as it involves needing a court document showing the name change (marriage certificates won't always work), then the national ID (domestic passport) has to be changed prior to changing the name on the external/international passport. It takes on average many weeks for the change on the domestic passport and has to be done in country. Add to that, many things such as property ownership, bank accounts, retirement, etc. are tied to the name on the domestic passport, and all those things have to be changed manually. Gotta love bureaucracy.
Good Luck!