Generative AI (genAI) is increasingly integrated across various sectors, yet laypeople often hesitate to adopt it due to factors such as unfamiliarity, uncertainty, or lack of skills. To address this, we apply a Design Science Research approach, reflecting on four past design projects in which we developed anthropomorphic conversational agents (CAs) tailored to laypeople. By incorporating human-like demographics, verbal behaviours, and non-verbal cues (e.g., emoticons, temporal delays), we aimed to enhance social presence, likeability, and perceived usefulness. Through evaluations using think-aloud studies and semi-structured interviews, we find that these anthropomorphic design elements facilitate acceptance but also reveal a dynamic evolution in user interaction – from initial hesitation to increased competence over time. This shifting engagement presents new challenges for interaction design and adaptivity related to genAI-based CAs. We derive five design principles that support the creation and management of adaptive experiences capable of responding to users’ evolving expertise levels. Our work advances HCI research by refining anthropomorphic design for laypeople, an underexplored aspect so far, and by illuminating the evolving complexity of human–AI engagement. Practically, our work help designing genAI-based CAs to lower adoption barriers, bridge the digital divide, and enable more inclusive, user-centred genAI-powered CAs that adapt over time, fostering long-term usability and broader accessibility in everyday contexts.