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Recent advancements in person recognition have raised concerns about identity privacy leaks. Gait recognition through millimeter-wave radar provides a privacy-centric method. However, it is challenged by lower accuracy due to the sparse data these sensors capture. We are the first to investigate a cross-modal method, IdentityKD, to enhance gait-based person recognition with the assistance of facial data. IdentityKD involves a training process using both gait and facial data, while the inference stage is conducted exclusively with gait data. To effectively transfer facial knowledge to the gait model, we create a composite feature representation using contrastive learning. This method integrates facial and gait features into a unified embedding that captures the unique identityspecific information from both modalities. We employ two distinct contrastive learning losses. One minimizes the distance between embeddings of data pairs from the same person, enhancing intraclass compactness, while the other maximizes the distance between embeddings of data pairs from different individuals, improving inter-class separability. Additionally, we use an identity-wise distillation strategy, which tailors the training process for each individual, ensuring that the model learns to distinguish between different identities more effectively. Our experiments on a dataset of 36 subjects, each providing over 5000 face-gait pairs, demonstrate that IdentityKD improves identity recognition accuracy by 6.5% compared to baseline methods.