If you have stored credit cards, they can buy tickets for anyone. They can change existing reservations. They can steal your passport number. All sorts of things.
You would be surprised. I work at an airline fraud prevention platform, and the legal hassle with credit card/loyalty fraud (which is what this would be) is so complex that fraudsters are often not charged with fraud. They just go ahead and provide their real information. Or change it right before takeoff at the airport, leaving the fraud analysts with no time.