The way to fix -that- issue is the same way every other business does it.
Require the name and address of the credit card to match exactly to the game's account holder.
In other words,
Jane Doe
123 Maple Lane
Ul'dah, Eorzea
12345
cannot use
John Smith
32 Privet Drive
Hogwart's, England
64321
credit card to buy her friend a mount.
Problem solved.
And the credit card processor SE uses (Inteligo? I think) DOES have the ability to compare them to make sure they match.
