It is commonly believed that borrowers cannot be anonymous in unsecured credit relations because anonymity heavily reduces the scope for punishment and therefore makes credit unfeasible except for very special circumstances. However, we demonstrate that credit is generally feasible even if borrowers are anonymous. In particular, we construct equilibria where borrowers use potentially multiple pseudonyms (such as usernames or wallet addresses) to interact with lenders. We assume that the complete history of past actions committed by a pseudonym is public but not the identity behind that pseudonym. While borrowers cannot be directly punished due to their anonymity, there is still scope for punishment. One possibility is based on the loss of reputation accumulated by a pseudonym over time. Another involves charging a fee to create pseudonyms. Although credit and anonymity are not mutually exclusive, we also show that maintaining a borrower's anonymity is costly.