My parents will be paying for my studies; how will the university understands that it will be my payment?

When you are making a payment, it is important to specify the customer code and the number of the invoice you have received. If you specify these codes, the payment will be assigned to the appropriate student.
If a bank employee asks for a study code doing a payment, the study code is 100, the payment code for bachelor's degree student is 110, master's degree - 120, executive master's degree - 130.