A useful general term that includes but is not specific to complaints is recipient.
Cambridge
recipient:
a person or organization that receives something, such as money, a prize, etc
a recipient of something
They are the country's biggest recipient of government funds.
As a grant recipient, you are required to write an annual report.
The recipient organization is responsible for monitoring expenditure.
One of many examples of the usage specific to complaints is in:
University of Bath
Recipients of informal student complaints are responsible for addressing them promptly and fairly. The recipient will normally let the student know (or arrange for a colleague to do so) within five working days of receiving the initial complaint what steps (if any) will be taken to address the complaint and the expected timescale, and advise to whom they should submit a formal complaint if they are dissatisfied with this outcome.