Robots operating in domestic and office environments must understand object ownership to correctly execute instructions such as ``Bring me my cup.'' However, ownership cannot be reliably inferred from visual features alone. To address this gap, we propose Active Ownership Learning (ActOwL), a framework that enables robots to actively generate and ask ownership-related questions to users. ActOwL employs a probabilistic generative model to select questions that maximize information gain, thereby acquiring ownership knowledge efficiently to improve learning efficiency. Additionally, by leveraging commonsense knowledge from Large Language Models (LLM), objects are pre-classified as either shared or owned, and only owned objects are targeted for questioning. Through experiments in a simulated home environment and a real-world laboratory setting, ActOwL achieved significantly higher ownership clustering accuracy with fewer questions than baseline methods. These findings demonstrate the effectiveness of combining active inference with LLM-guided commonsense reasoning, advancing the capability of robots to acquire ownership knowledge for practical and socially appropriate task execution.