Firm reputation plays a vital role in financial networks, and it is especially impactful in times of market stress or a financial crisis. This paper uses a novel theoretical model to study reputational dynamics in financial networks, taking into account that firms begin with incomplete information, learn about others over time, and update their connections as their beliefs evolve. In our model, stronger firms develop high reputations and remain in the network, while weaker firms will eventually drop in reputation and get shut out. We show that more information revelation during crisis generally increases network fragility and harms social welfare. It is thus crucial to maintain anonymity among firms during a crisis. Certain network structures, such as core-periphery networks, are more systemically resilient against negative informational effects.