Decentralized federated learning (DFL) enables collaborative model training across edge devices without centralized coordination, offering resilience against single points of failure. However, statistical heterogeneity arising from non-identically distributed local data creates a fundamental challenge: nodes must learn personalized models adapted to their local distributions while selectively collaborating with compatible peers. Existing approaches either enforce a single global model that fits no one well, or rely on heuristic peer selection mechanisms that cannot distinguish between peers with genuinely incompatible data distributions and those with valuable complementary knowledge. We present Murmura, a framework that leverages evidential deep learning to enable trust-aware model personalization in DFL. Our key insight is that epistemic uncertainty from Dirichlet-based evidential models directly indicates peer compatibility: high epistemic uncertainty when a peer's model evaluates local data reveals distributional mismatch, enabling nodes to exclude incompatible influence while maintaining personalized models through selective collaboration. Murmura introduces a trust-aware aggregation mechanism that computes peer compatibility scores through cross-evaluation on local validation samples and personalizes model aggregation based on evidential trust with adaptive thresholds. Evaluation on three wearable IoT datasets (UCI HAR, PAMAP2, PPG-DaLiA) demonstrates that Murmura reduces performance degradation from IID to non-IID conditions compared to baseline (0.9% vs. 19.3%), achieves 7.4$\times$ faster convergence, and maintains stable accuracy across hyperparameter choices. These results establish evidential uncertainty as a principled foundation for compatibility-aware personalization in decentralized heterogeneous environments.