Because a telepresence robot is intended for use in telecommunications, conveying the presence of a remote sender is an important issue. Even though certain characteristics of robots such as identity could be effective at generating a sense of presence, this risks yielding a distortion of presence in the remote sender. Thus, in order to find effective ways to increase presence, we executed an experiment comparing a telepresence robot with high identity and a telepresence robot with low identity. The 60 participants in this study engaged in a video call with a remote sender using either a telepresence robot with high identity or a telepresence robot with low identity. The results showed that participants felt more remote sender presence when interacting with the telepresence robot with low identity than they did with the one with high identity. On the other hand, when a telepresence robot has high identity, participants felt more presence toward the robot than they did toward the one with low identity. In the second study (N=72), participants experienced two types of telepresence robots (identity level: a telepresence robot with high identity vs. a telepresence robot with low identity) with two types of remote senders (number of remote senders: single remote sender vs. multiple remote senders). The identity level of the robot and the number of remote senders affected the presence of the remote sender, telepresence, and the presence of the robot. We discuss in detail the implications for the design of telepresence robots in terms of increasing presence.