I don't think there is a default profit and loss statement per customer. But you can use this default P&L report in another way to achieve the customer wise P&L. Enable Analytic Accounting in the settings. Create an Analytic Account whenever you are creating a new customer. Now at the time of any transaction (income or expense), you can choose the customer's related analytic account.
Now in the P&L Reporting, you will have option to filter by Customer or the Analytic Account.