If you haven’t added a delivery method Click & collect yet, learn how to do it here. It will be needed to complete the settings of this payment method.
Go to Settings > Payments > Click on + Payment method.
Click on Custom payment method.
Add the name for this payment method: Payment on pickup.
Change the message template. This message is displayed when the order is placed.
Remove from the message, for example, information about the bank account number and add a few sentences related to the personal pick up of the order.
Finally, choose the type of delivery you want to have for this payment method. You should typically select the option of personal pickup, click & collect.
If you would like to add a payment for cash on delivery, check this article.