Under Client Config > Marketing: Giftcards > Required Fields choose any of Name, Email and Phone. The gift card page then refuses Add to cart until they are filled, showing tooltips such as "Name is required", "Email is required" (must be a valid address) or "Phone is required". When Allow Shipping is on, the email and phone requirements only apply to digital cards; physical cards use the address fields instead. Note that if Email is not required and the buyer leaves it blank, no recipient email can be sent — the card then only exists in the admin list.