Automated vehicles (AVs) face a critical need to adopt socially compatible behaviors and cooperate effectively with human-driven vehicles (HVs) in heterogeneous traffic environment. However, most existing lane-changing frameworks overlook HVs' dynamic trust levels, limiting their ability to accurately predict human driver behaviors. To address this gap, this study proposes a trust-aware game-theoretic lane-changing decision (TGLD) framework. First, we formulate a multi-vehicle coalition game, incorporating fully cooperative interactions among AVs and partially cooperative behaviors from HVs informed by real-time trust evaluations. Second, we develop an online trust evaluation method to dynamically estimate HVs' trust levels during lane-changing interactions, guiding AVs to select context-appropriate cooperative maneuvers. Lastly, social compatibility objectives are considered by minimizing disruption to surrounding vehicles and enhancing the predictability of AV behaviors, thereby ensuring human-friendly and context-adaptive lane-changing strategies. A human-in-the-loop experiment conducted in a highway on-ramp merging scenario validates our TGLD approach. Results show that AVs can effectively adjust strategies according to different HVs' trust levels and driving styles. Moreover, incorporating a trust mechanism significantly improves lane-changing efficiency, maintains safety, and contributes to transparent and adaptive AV-HV interactions.