Pretty sure the credit card number is the important issue, not the exact name.

They want to see that the person who used that credit card (number) to buy the tickets actually has possession of that physical card.

BTW I purchase all my TG flights online and have only been asked to show the purchasing CC several times. But I always have it with me ... just in case.

It's an annoying policy, especially for people whose flights may be purchased for them by other people.