Given the fact that the receiving official may be the COR or may be a warehouse staffer, end user, or other designated government personnel coupled with the fact that inspection and receiving reports will be sources of documentation of the quality and timeliness of the contractor's performance. Who specifically designates the warehouse staffer, end user, or other designated government personnel if other than the COR.
Good question. FAR 1.602-1(a) reads "Contracting officers have authority to enter into, administer, or terminate contracts and make related determinations and findings..."
A recieving report is something used to document that inspection (quality assurance) has been done and/or acceptance (or both) and these fall under "administer" as they are part of the contract administration function. Ultimately it is the contracting officer's responsibility to delegate the authority to perform these functions. This is normally done through a letter of delegation to a COR or a CAO (contract administration office).
That said, there are many scenarios (e.g. one time commercial supplies, etc.) when the contract or order is not delegated to a CAO or COR. In these instances the documentation is not formal and could be done orally or as a matter of standard operating procedures. If electronic payment is being made; the individual who processes the request in PIEE (WAWF module) is the one who is "accepting" for the government. The recieving report, if separate from PIEE, is just the source documentation.
Update 9/22/2020: Additional information on inspection and acceptance (and documentation requirements) can be found at FAR subparts 46.4 and 46.6 as well as DFARS subparts 246.4 and 246.6.