Without the correct number, you can’t even gain access to an agent or an operator. The Booking.com website showed my tickets as “canceled” with a refund due of $16. But I paid $589 for them.

This means you’ll be provided a valid passenger name record (PNR) number, but your reservation will not be “ticketed”—meaning no e-ticket number—until the full fare is paid.

But when her airline canceled her flight and she couldn’t get through to the EZAir department by phone, she had to pay $1,517 for new tickets. So much for the guarantee.

However, if you’d like to change the full name on a ticket, some airlines, like Delta Air Lines, do not allow it, as tickets are considered nontransferable. Others, such as Frontier Airlines ...