Yup. When I was sightseeing in Israel about five years ago, we were warned about crossing the border into Egypt in order to see Mount Sinai. It would have been dangerous to have Israel's stamp already on our passport as normal Americans.
And we're supposed to believe that the CIA sent a spy into a dangerous region with his real identity? And written down on a passport stamped by the Israeli's, no less? If they had caught a CIA spy, they would have never known his name.
Infiltrating terrorists groups is a very difficult thing to do. They need to see many years of contact with the group before they will trust anyone.
I can see a student that has already made contact with some middle eastern types in college continuing his identity in order to keep the contact.
This isn't the cold war, where James Bond gets assigned a new identity for every mission. Terrorists just don't operate that way.
I wouldn't doubt that the only way we will EVER get a spy into their network is to recruit someone already in the group, who will continue to use their own name. If Berg made contact with these creeps in college, then he'd continue using his own name.