The rapid advancement of customized Large Language Models (LLMs) offers considerable convenience. However, it also intensifies concerns regarding the protection of copyright/confidential information. With the extensive adoption of private LLMs, safeguarding model copyright and ensuring data privacy have become critical. Text watermarking has emerged as a viable solution for detecting AI-generated content and protecting models. However, existing methods fall short in providing individualized watermarks for each user, a critical feature for enhancing accountability and traceability. In this paper, we introduce PersonaMark, a novel personalized text watermarking scheme designed to protect LLMs' copyrights and bolster accountability. PersonaMark leverages sentence structure as a subtle carrier of watermark information and optimizes the generation process to maintain the natural output of the model. By employing a personalized hashing function, unique watermarks are embedded for each user, enabling high-quality text generation without compromising the model's performance. This approach is both time-efficient and scalable, capable of handling large numbers of users through a multi-user hashing mechanism. To the best of our knowledge, this is a pioneer study to explore personalized watermarking in LLMs. We conduct extensive evaluations across four LLMs, analyzing various metrics such as perplexity, sentiment, alignment, and readability. The results validate that PersonaMark preserves text quality, ensures unbiased watermark insertion, and offers robust watermark detection capabilities, all while maintaining the model's behavior with minimal disruption.