I understand the government would not give out names of people eavesdropped on, but why should the programs be classified? So the terrorists don't know the NSA is trying to eavesdrop on them?

Would any al Qaeda member really think their bank accounts, emails and phone calls were safe? No. The only reason I can imagine is to keep the American people in the dark. Oh, and to escape judicial oversight, as the recent ACLU v NSA case showed. If you can't prove the program exists, you can't fight it.