I checked the Customer Eligibility checkbox, but I was able to use the unique coupon code issued for another person. What other settings do I need to make so that only the person who received the coupon code can use it?
This is the only setting needed to ensure that only the person who received the discount code can use it. Another person may still be able to enter the discount code, and see a reduced price. However, when the other person fills in the checkout form, then Shopify will inform that the discount code is not valid. It will also revert the original price.