Human Digital Twins (HDTs) have traditionally been conceptualized as data-driven models designed to support decision-making across various domains. However, recent advancements in conversational AI open new possibilities for HDTs to function as authentic, interactive digital counterparts of individuals. This paper introduces a novel HDT system architecture that integrates large language models with dynamically updated personal data, enabling it to mirror an individual's conversational style, memories, and behaviors. To achieve this, our approach implements context-aware memory retrieval, neural plasticity-inspired consolidation, and adaptive learning mechanisms, creating a more natural and evolving digital persona. The resulting system does not only replicate an individual's unique conversational style depending on who they are speaking with, but also enriches responses with dynamically captured personal experiences, opinions, and memories. While this marks a significant step toward developing authentic virtual counterparts, it also raises critical ethical concerns regarding privacy, accountability, and the long-term implications of persistent digital identities. This study contributes to the field of HDTs by describing our novel system architecture, demonstrating its capabilities, and discussing future directions and emerging challenges to ensure the responsible and ethical development of HDTs.