Protecting speaker identity is crucial for online voice applications, yet streaming speaker anonymization (SA) remains underexplored. Recent research has demonstrated that neural audio codec (NAC) provides superior speaker feature disentanglement and linguistic fidelity. NAC can also be used with causal language models (LM) to enhance linguistic fidelity and prompt control for streaming tasks. However, existing NAC-based online LM systems are designed for voice conversion (VC) rather than anonymization, lacking the techniques required for privacy protection. Building on these advances, we present Stream-Voice-Anon, which adapts modern causal LM-based NAC architectures specifically for streaming SA by integrating anonymization techniques. Our anonymization approach incorporates pseudo-speaker representation sampling, a speaker embedding mixing and diverse prompt selection strategies for LM conditioning that leverage the disentanglement properties of quantized content codes to prevent speaker information leakage. Additionally, we compare dynamic and fixed delay configurations to explore latency-privacy trade-offs in real-time scenarios. Under the VoicePrivacy 2024 Challenge protocol, Stream-Voice-Anon achieves substantial improvements in intelligibility (up to 46% relative WER reduction) and emotion preservation (up to 28% UAR relative) compared to the previous state-of-the-art streaming method DarkStream while maintaining comparable latency (180ms vs 200ms) and privacy protection against lazy-informed attackers, though showing 15% relative degradation against semi-informed attackers.