If you are using the totally free version of PayPal processing, Users are not required to establish an account with PayPal, but they are offered the opportunity to do so.
However, since all payments are transacted off your site and within the secure PayPal site, they are treated as "non-recurring transactions" unless they have previously established an individual PayPal account ..... if they have established one, they will have the ability to recall all invoices/payments made with that account, which would show not only all payments made to you, but every other seller as well.

The only way to establish (and manage) client accounts is to use a real cart foundation, which has the coding pre-installed to operate with PayPal and Merchant Account processing as well.
.