I'm not sure what you are hinting at by saying "like a potential criminal who may be using someone else's card." Were you using someone else's card or not? Its a membership based store and your card is what validates that status. What exactly was the scenario you found yourself in? maiden vs. married name? Picture scratched up?
It looks like from reviews left that the Costco Shop gift card[1] is a one time use. How they would know that, maybe via system tracking, I'm not sure. It would seem that you would have to have a new card every time you go verse a single card with $3k on it. Other reviews seem to indicate that they check the member that gave you the card which after the first year of renewal you would not be able to show since your membership lapsed.
It looks like from reviews left that the Costco Shop gift card[1] is a one time use. How they would know that, maybe via system tracking, I'm not sure. It would seem that you would have to have a new card every time you go verse a single card with $3k on it. Other reviews seem to indicate that they check the member that gave you the card which after the first year of renewal you would not be able to show since your membership lapsed.
[1] https://www.costco.com/costco-shop-card.product.10024438.htm...