Do I have to prove my identity with an exchange to be a creator?
Yes you do.
Because Brave is classified as a revenue sharing business they have to adhere to AML (anti-money laundering) laws of a number of different countries. So they must KYC anyone who earns real value from Rewards, which includes all creators.
Note that Brave do not have access to any of the documents you submit to your exchange during the KYC process. Brave only requires that the partner exchange verifies that you are a real individual.