You must register a domain for one of your customer, but you are the one who sets the billing side.
To do this, you must first create an additional contact via your customer account: https://my.planethoster.net/client-area/add-contact
Then you can order the domain via the page: https://my.planethoster.net/domains/new
In the form, you can change “Domain Owner Information” to that of your customer.
Place the order and the domain owner will be in the name of the additional contact.