Vietnam’s traditional medical texts were historically written in Classical Chinese using Sino-Vietnamese pronunciations. As the Vietnamese language transitioned to a Latin-based national script and interest in integrating traditional medicine with modern healthcare grows, accurate translation of these texts has become increasingly important. However, the diversity of terminology and the complexity of translating medical entities into modern contexts pose significant challenges. To address this, we propose a method that fine-tunes large language models (LLMs) using augmented data and a Hybrid Entity Masking and Replacement (HEMR) strategy to improve named entity translation. We also introduce a parallel named entity translation dataset specifically curated for traditional Vietnamese medicine. Our evaluation across multiple LLMs shows that the proposed approach achieves a translation accuracy of 71.91%, demonstrating its effectiveness. These results underscore the importance of incorporating named entity awareness into translation systems, particularly in low-resource and domain-specific settings like traditional Vietnamese medicine.