You will have to click the link that leads to their payment page. The information will show up there which payment processor is being used. That is of course if I am not misunderstanding your question.
While there may be a few tricks, depending on how the site is set up, the basic answer is not usually. Unless they redirect you to a site that is owned by the processor, credit cards are processed internally on the server. Why on Earth would you want this information?
How does that help? If the credit cards are processed internally on the server, there would be no way to see this.
Yes, most website are not PCI-Compliant and can not process internally, even though, most of them leave tracks of the used payment gateway.