Recently, mechanism design without monetary transfers is attracting much attention, since in many application domains on Internet, introducing monetary transfers is impossible or undesirable. Mechanism design studies how to design mechanisms that result in good outcomes even when agents strategically report their preferences. However, in highly anonymous settings such as the Internet, declaring preferences dishonestly is not the only way to manipulate the mechanism. Often, it is possible for an agent to pretend to be multiple agents, and submit multiple reports using different identifiers, e.g., different e-mail addresses. Such false-name manipulations are more likely to occur in a mechanism without monetary transfers, since submitting multiple reports would be less risky in such a mechanism. In this paper, we formalize false-name manipulations in facility location problems on the real line and discuss the effect of such manipulations.