Thanks for your suggestions!
It turned out to be still weird, but not a problem:
The mobile checkin had my name wrong as well, and so I wasn't able to complete the process. Got to the airport, and suddenly the checkin terminal had the name right again.
In the end even the Precheck clearance came through as if nothing ever happened, which tells me that the "core system" of US must have had my name right all along.
So, all this is still very weird, but I am about to board and all things turned out well.