In a written exam they can cover the names - give you a random number as you enter the room and you write that on the paper, and but your name and number on a different paper. You also need to type everything out on a computer with spell check. (and even then if you write bucket or pail will identify you but it is unlikely any professor knows you well enough to tell those)

When you audition for a symphony you perform behind a curtain and are required to wear soft slippers (so they can't tell if you are a wearing high heals - female).

We can probably use voice changers so the examiner cannot tell who you are by your voice, but those tend to be fatiguing.