The proliferation of misinformation within multi-Large Language Model (LLM) agent systems presents unprecedented challenges for AI safety research and deployment. Traditional epidemiological models, particularly the Susceptible-Infected-Susceptible (SIS) framework, provide computational efficiency but fundamentally fail to capture the sophisticated cognitive processes and emergent collective behaviors that characterize modern AI agent interactions. These limitations become particularly problematic when analyzing safety-critical phenomena such as echo chamber formation, semantic drift, and the propagation of contested information across agent networks. This research introduces a comprehensive theoretical framework based on Metropolis-Hastings Naming Games (MHNG) that models belief propagation through decentralized Bayesian inference mechanisms. Our brain-inspired, agent-centric approach transcends the limitations of traditional epidemic metaphors by explicitly incorporating belief revision processes, semantic negotiation dynamics, and heterogeneous agent utility functions. The proposed framework provides detailed mathematical formalization of MHNG adapted specifically for belief dynamics in LLM agent populations, including novel LLM-driven utility evaluation mechanisms and adaptive belief update protocols. Through rigorous theoretical analysis and comprehensive experimental validation using multi-dimensional safety metrics, we demonstrate MHNG’s superior representational capacity for safety-critical scenarios. The framework naturally models slower convergence rates for contested information, facilitates the emergence of monitorable belief clusters, and provides mechanistic insights into the formation of opinion polarization. Computational experiments reveal significant improvements in misinformation resistance (from 0.21 to 0.79) while maintaining high truth propagation efficiency (0.98), establishing a principled foundation for advancing AI safety analysis in complex multi-agent ecosystems.