A bit more information is needed.
Presumably there could be several exams going on at the same time, hence a risk that one person is accidentally scheduled to invigilate in two places at once.
Will you have a timetable for each exam room?
If so, use a separate sheet for each exam room,
Each sheet should be identical in layout, with time periods throughout the working day and rows for name of exam taking place in each time period and the name of the invigilator for each time period.
You then add one more sheet with the same format of time periods, and which has a formula in each time period which tests that time slot (cell) in each room(sheet), for duplicate names.
As suggested by kakarukeys use data validation for entering invigilator names to ensure that you don't miss double booking, because of a typo in the name.
If there are a lot of exam rooms, a formula to test for no duplicates may become too complex and a macro to undertake the test may be appropriate, so please provide more details.