Agent systems deployed in dynamic environments continuously update their memories, skills, and runtime configurations, leading to evolving trajectories and challenges for persistent identity authentication. Existing text and agent watermarking methods struggle to achieve stable watermark embedding under dynamic environments, while embedded watermarks may become difficult to recover due to environmental changes. This paper proposes DASMark, an identity watermarking framework for dynamic agent systems. DASMark introduces Action-Preserving Embedding (APE), which learns semantically similar but distinguishable decision-expression channels from diverse interaction trajectories to enable stable watermark embedding in dynamic systems. It further introduces Shift-Robust Recovery (SRR) to mitigate context-induced shifts and improve watermark recovery stability under dynamic environments. In dynamic settings, DASMark achieves 98.5% bit-decoding accuracy and maintains 95.2% accuracy under attack scenarios, while preserving task utility comparable to unwatermarked agents.

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