The best response is:

a. You should NOT tell him your full name and what school you go to.

It is never a good idea to tell a stranger your full name, where you go to school, where you live, or any other personal information until you know that you can trust the person. It is a good idea to end the conversation, call to be picked up, or speak with a security guard if you feel uncomfortable. Do not worry about sounding rude or being wrong about someone. It is always better to be on the safe side.