This paper presents a survey and taxonomy of LLM fingerprinting and watermarking for identity, ownership verification, provenance, and generated-content attribution. Large language models (LLMs) require substantial investments in data, computation, and expertise, and are increasingly deployed in high-stakes settings, making it critical to protect LLM-related assets and trace their origins. Existing work has rapidly expanded across dataset provenance, model ownership, and generated-content detection, but the field remains fragmented: fingerprinting and watermarking are often used inconsistently, and methods are typically studied within isolated asset-specific settings. To address this gap, we introduce implicit identity as a unifying abstraction for verifiable but not directly observable identity signals in LLM systems. We distinguish fingerprinting as non-intrusive identity derived from intrinsic characteristics, and watermarking as intrusive identity deliberately embedded into data, models, or generated content. We then propose a lifecycle-based taxonomy that organises techniques across datasets, models, and generated content, and further separates them by verification semantics: similarity-based attribution and keyed verification. Finally, we establish an evaluation framework centred on identifiability, robustness, and deployability, summarising representative metrics under realistic access and transformation regimes. By unifying terminology, lifecycle stages, and evaluation objectives, this survey provides a structured foundation for studying LLM identity technologies and for developing more reliable mechanisms for asset protection and provenance.