Students whose names have been called may begin the exam.
Literal
Name [object-を] called student [topic-は] exam [object-を] begin please.
A nice example of a Japanese relative clause: 名前を呼ばれた学生 = 'student whose name was called.' No relative pronoun — the entire clause attaches directly to 学生. Passive 呼ばれた makes the student the one who was called, while 名前 is the thing that was the target of the calling.