Royalty payments are driven by the registration of the songs. So, if a work is registered as "by composer X" (and this can only be done by X in person or by their agent/publishing company), then that is where the royalty payments will go, whether from airplay etc (PRS in the UK) or new recordings (MCPS in the UK). The fact that the work may be wrongly attributed to Y instead of X on the CD cover may lead a DJ playing the piece to declare it as a work by Y in the PRS submission, but that will nevertheless be automatically checked against their database and corrected, or at worst it will go into the "unresolved" files, which every registered artist/composer has access to, and they can correct it there.