In this study, we propose a method to give a personality to a spoken dialogue agent and evaluate its efficiency. We propose a model that explains personality cognition process through dialogue and investigate its validity. Recently, some research studies in Human-Agent Interaction (HAI) showed that controlling non-verbal information gives some personalities to the agents. However, we consider that verbal information sent from an agent might also contribute to give a personality to it self. In this paper, we focus on self-disclosures as an important factor of giving a personality, and analyze the effects of self-disclosures on giving a personality to the agent by evaluation of impressions. We found these things that self-disclosure is effective for making a user cognizes a personality of the agent, self-disclosures of the agent perform the same as those of human, and humanlike self-disclosures does not impede personality cognition even if a agent utters them. In addition, we verified that our proposed approach gave some distinct personalities.