[make] a complaint

to express dissatisfaction or criticism about something

If you are unsatisfied with your purchase, you can make a complaint to the customer service department.
She decided to make a complaint to the restaurant manager about the quality of her meal.
He made a formal complaint to the HR department regarding workplace harassment.
When the hotel room wasn't clean, they had no choice but to make a complaint at the front desk.
If you receive a damaged product, you should make a complaint to the shipping company.