I see your point.I would call it "the receipt." Written confirmation of payment for anything is a receipt.
English used to have a whole pile of bureaucratic phrases for receipts specific to one type of transaction: There seems to have been a movement away from this and towards (except where absolutely necessary) the use of a descriptive adjectival phrase - in your case "The receipt for the deposit."
We do over here, but we don't call it depositing. We might hand over or mail a cheque, but increasingly this method is becoming less popular.Over here I don't think we generally deposit money into someone else's account
I would call it a deposit slip stamped by the bank.If a student makes the payment for his private lessons by deposit, the paper he sends the teacher to prove that is called the deposit confirmation, payment receipt or is there another name that would be more appropriate?