This article analyzes entry–exit decisions in a market where reputation determines the price that firms may charge, within a rational‐expectation model of competition in a nonatomic market under heterogeneous reputations. The analysis focuses on the class of name‐switching reputational equilibria, in which a firm discards its name if and only if its reputation falls below the entrants' reputation. The main technical result is the existence of a unique steady‐state equilibrium within this class, in which the entrants' reputation is endogenous. The resulting industry dynamics is largely on agreement with the findings in the empirical literature.