A company's brand identity is vital for fostering meaningful interactions with customers in a digital economy. As generative artificial intelligence (GenAI) becomes increasingly integrated into our daily lives, AI-based assistants are evolving into the primary channel for representing a brand's identity. Consequently, brand departments face the challenge of translating their company's brand identity into highly interactive AI-based assistants effectively. While there is diverse research on single cues that influence user perceptions, the literature lacks a comprehensive understanding of conversational cues and their impact on brand-related outcomes. Hence, we conduct a systematic literature review to identify verbal and visual cues in the design of AI-based chatbots and examine how they influence the perceptions of the assistants and the brand. We contribute a conceptual framework that summarizes the independent and dependent variables as well as their interrelationships and provides researchers and practitioners with a basis for designing and studying conversational design in the age of GenAI.