How should a companion robot behave? In this research, we present a cognitive architecture based on a tailored personality model to investigate the impact of robotic personalities on the perception of companion robots. Drawing from existing literature, we identified empathy, trust, and enjoyability as key factors in building companionship with social robots. Based on these insights, we implemented a personality-dependent, emotion-aware generator, recognizing the crucial role of robot emotions in shaping these elements. We then conducted a user study involving 84 dyadic conversation sessions with the emotional robot Navel, which exhibited different personalities. Results were derived from a multimodal analysis, including questionnaires, open-ended responses, and behavioral observations. This approach allowed us to validate the developed emotion generator and explore the relationship between the personality traits of Agreeableness, Extraversion, Conscientiousness, and Empathy. Furthermore, we drew robust conclusions on how these traits influence relational trust, capability trust, enjoyability, and sociability.