Upvote:2
If your boyfriend has any TSA accepted ID that has the name as listed on the reservation, he can use that.
Barring that, I'm afraid you may be charged a fee by Delta to change the name on the ticket; as you cannot fly if the name doesn't match that on the ID you are using to identify yourself.
There are some exceptions (like if the first/last name is switched - a common issue); but in your case its a completely different name.
Its like saying Burhan Khalid wants to travel on a ticket issued to Burhan Jones.