When the airline does want to see the card, it's not to identify the passenger, it's to make sure the card use was legit. On occasions when I ran into this problem, I just stopped by the airport ahead of the trip and showed them the card. If this is an issue, they only need to verify the cardholder before the trip - it doesn't have to be at boarding.
But it may not even be an issue - if it is, it will be flagged on the record and the agent should be able to tell you and help you resolve it ahead of time. You also should have been notified of this requirement during booking.
I had one case where I was traveling with a youth group and one of the parents had not done this (even though we had instructed every parent to check). I ended up having to pay for a new ticket (though the airline did honor the previous price) and get reimbursed later by the parent (who had the previous ticket value refunded to his card).