If bitcoin is converted to fiat money on an exchange, the exchange has irrefutable knowledge of your identity because they require the account name and bank account name to match.
The only way to anonymize a withdrawal of bitcoin-converted fiat would be to first transfer a non-exchange bitcoin wallet to the exchange-based bitcoin wallet using a bitcoin tumbler or mixer so that it looks clean. It would longer matter whether account names match to the withdrawer because the exchange, at least, would no longer know the real source of the funds. However, the fiat is still associated with your name. So the tumbler approach is not really anonymization, but merely anonymization of the source.
How else can bitcoin-sourced fiat be withdrawn anonymously?