This depends. Purchasing stablecoins with cryptocurrency on a decentralized exchange (or a centralized exchange in which the user has not completed KYC) can be relatively anonymous. However, users looking to purchase (or redeem) stablecoins with fiat currencies directly from their respective issuers will need to complete the standard KYC (Know Your Customer) and AML requirements. If anonymity is the priority, Blockfer recommends using DAI - the most decentralized stablecoin currently available.