Let me give you a scenario.
The person who lives next door, who is next to you on the bus every day, who works with you, is a good friend, etc, etc is a very deserving person. They do not have the finances to visit a long lost friend, a dying mother, a lost love, etc etc. You decide to help them by making the trip available and possible for them, simply by buying them a ticket.
They would never accept the generosity from you if asked to have a free ticket, they would return it if they knew who it came from. So the ticket really does need to be incognito.
You could come to a website like Future.Travel and book the flight for them. The passengers name would be there as they are the traveller, the contact person for the booking could be Santa Claus with an address of the North Pole. The email address would need to be the travellers, in order for the e-ticket to arrive to them.
For payment, pay with cash in more than 30 countries, or use Bitcoin in more than 200 countries. No credit card to track the transaction, so your philanthropic identity is completely unknown to the receiver.
Pay it forward. ❤