The recent success of large language models (LLMs) has attracted widespread interest to develop role-playing conversational agents personalized to the characteristics and styles of different speakers to enhance their abilities to perform both general and special purpose dialogue tasks. However, the ability to personalize the generated utterances to speakers, whether conducted by human or LLM, has not been well studied. To bridge this gap, our study introduces a novel evaluation challenge: speaker verification in agent-generated conversations, which aimed to verify whether two sets of utterances originate from the same speaker. To this end, we assemble a large dataset collection encompassing thousands of speakers and their utterances. We also develop and evaluate speaker verification models under experiment setups. We further utilize the speaker verification models to evaluate the personalization abilities of LLM-based role-playing models. Comprehensive experiments suggest that the current role-playing models fail in accurately mimicking speakers, primarily due to their inherent linguistic characteristics.