hide somebody's identity
conceal somebody's identity

I am not certain whether it is so important here to hide my identity.

He had kept an entire identity hidden, so how could she trust him now?

There was no point in hiding her identity, she thought.

And no real attempt was made to hide her identity.

In fact, he has another identity hidden from other competitors.

"Pretty hard to not say that you survived, but we can probably hide your identity."

But it only allowed women to stay in the country for one year and did nothing to hide their identities.

Then he said, 'I don't suppose there would be much point in hiding my true identity from you.

Had he hidden her identity from the others to protect his own reputation?

For those that need to hide their identity they use masks.