Who assigns a particular auditor? The MDSAP AO or RA?

It is the AO’s responsibility to assign auditors for individual audits of medical device manufacturers, taking into account their competence, impartiality and availability. 

Unlike other certification programs, a manufacturer may not oppose the choice of the auditor under the MDSAP (IMDRF MDSAP WG N3 Requirements for Medical Device Auditing Organizations for Regulatory Authority Recognition exception to ISO /IEC 17021-1, section 9.2).