Large Large Language Models (LLMs) are increasingly integrated into diverse industries, posing substantial security risks due to unauthorized replication and misuse. To mitigate these concerns, robust identification mechanisms are widely acknowledged as an effective strategy. Identification systems for LLMs now rely heavily on watermarking technology to manage and protect intellectual property and ensure data security. However, previous studies have primarily concentrated on the basic principles of algorithms and lacked a comprehensive analysis of watermarking theory and practice from the perspective of intelligent identification. To bridge this gap, firstly, we explore how a robust identity recognition system can be effectively implemented and managed within LLMs by various participants using watermarking technology. Secondly, we propose a mathematical framework based on mutual information theory, which systematizes the identification process to achieve more precise and customized watermarking. Additionally, we present a comprehensive evaluation of performance metrics for LLM watermarking, reflecting participant preferences and advancing discussions on its identification applications. Lastly, we outline the existing challenges in current watermarking technologies and theoretical frameworks, and provide directional guidance to address these challenges. Our systematic classification and detailed exposition aim to enhance the comparison and evaluation of various methods, fostering further research and development toward a transparent, secure, and equitable LLM ecosystem.