No.
Rolls Royce remains a separate company, that makes aircraft engines.
Volkswagen owns the entirety of the automotive manufacturing business that was once owned and operated by Rolls Royce. Through this operation, they make Bentleys. They do not have the rights to use the Rolls Royce name or logo.
BMW has licensed the rights from Rolls Royce to use the name and logo on automobiles, which they build at a factory that they set up for this purpose.
Before the latest breakup, Bentleys and Rolls Royces used to be made side-by-side, at the same factory, with each model under one brand being almost identical to a corresponding model under the other. From a very long time ago (late 1970s or early 1980s), I recall being made aware that the difference in price between a Rolls Royce and an otherwise identical Bentley was about $600 (out of a car selling, then, for over $100,000), and that this directly reflected the difference in manufacturing costs between the Rolls Royce grille and the Bentley grille.