Payment method is set as "Link" for CC orders

[annemirasol]

Describe the bug
When Link is enabled, and the user is logged in, the Payment Method shows as "Link" in several places for orders purchased via credit card.

To Reproduce
Steps to reproduce the behavior:

1. As the merchant, enable Link as a payment method.
2. As a guest shopper, purchase something using a credit card.
3. Notice the order confimation page shows "Credit / Debit Card" as the payment method.
4. As a logged in shopper, purchase something using a credit card.
5. Notice the order confirmation shows "Link" as the payment method.
6. As the merchant, view the order details page. Notice that the second order shows "via Link" in the order totals section. (See screenshot below)

Expected behavior
I expected to see "Credit / Debit Card" as the payment method.

Screenshots

For this order, I was a logged in user, and paid via a manually entered (i.e. not a saved payment method) credit card.

Confirmation page shows Payment method as "Link".

Notice the Order details page correctly shows payment as via "Credit/ debit card"...

...but in the payment details section, it incorrectly shows "via Link"