Hmm its not quite that straight forward.

AFAICR - There are two "Rolls Royce" companies.

One makes the cars you know as Rolls Royces.

The other owns the rights to the RR name.

VW bought one company and BMW the other.

I think BMW has the company that makes the cars, and VW bought the company with the naming rights [much to BMW's chagrin].

Which is why BMW officially now makes Bentleys and not Rolls Royces as while the RR and Bentley cars used to be pretty much the same, BMW doesn't have the rights to the RR name so cannot sell them as such.

I got all this from a BBC motoring program (The Cars the Star?) a few months back.
I may have got VW and BMW mixed up in their roles and who owns what, but the fact is one company has the factory the other the rights to the name.