As conversational AI systems become more realistic and widely deployed, users are increasingly uncertain about whether they are interacting with a human or an AI system. When AI identity is unclear, users may unwittingly share sensitive information, place unwarranted trust in AI-generated advice, or fall victim to AI-enabled fraud. More broadly, a persistent lack of transparency can erode trust in mediated communication. While regulations like the EU AI Act and California's BOT Act require AI systems to identify themselves, they provide limited guidance on reliable disclosure in real-time conversation. Existing transparency mechanisms also leave gaps: interface indicators can be omitted by deployers, and provenance tools require coordinated infrastructure and cannot provide reliable real-time verification. We ask how conversational AI systems should maintain identity transparency as human-AI interactions become more ambiguous and diverse. We advocate for disclosure by design, where AI systems explicitly disclose their artificial identity when directly asked. Implemented as model behaviour, disclosure can persist across deployment contexts without relying on user interfaces, while preserving user agency to verify identity on demand without disrupting immersive uses like role-playing. To assess current practice, we present the first multi-modal (text and voice) evaluation of disclosure behaviour in deployed systems across baseline, role-playing, and adversarial settings. We find that baseline disclosure rates are often high but drop substantially in role-play and can be suppressed under adversarial prompting. Importantly, disclosure rates vary significantly across providers and modalities, highlighting the fragility of current disclosure behaviour. We conclude with technical interventions to help developers embed disclosure as a fundamental property of conversational AI models.