Online anomaly detection (OAD) plays a pivotal role in real-time analytics and decision-making for evolving data streams. However, existing methods often rely on costly retraining and rigid decision boundaries, limiting their ability to adapt both effectively and efficiently to concept drift in dynamic environments. To address these challenges, we propose DyMETER, a dynamic concept adaptation framework for OAD that unifies on-the-fly parameter shifting and dynamic thresholding within a single online paradigm. DyMETER first learns a static detector on historical data to capture recurring central concepts, and then transitions to a dynamic mode to adapt to new concepts as drift occurs. Specifically, DyMETER employs a novel dynamic concept adaptation mechanism that leverages a hypernetwork to generate instance-aware parameter shifts for the static detector, thereby enabling efficient and effective adaptation without retraining or fine-tuning. To achieve robust and interpretable adaptation, DyMETER introduces a lightweight evolution controller to estimate instance-level concept uncertainty for adaptive updates. Further, DyMETER employs a dynamic threshold optimization module to adaptively recalibrates the decision boundary by maintaining a candidate window of uncertain samples, which ensures continuous alignment with evolving concepts. Extensive experiments demonstrate that DyMETER significantly outperforms existing OAD approaches across a wide spectrum of application scenarios.