5G-Advanced (5G-A) has enabled the vibrant development of low altitude integrated sensing and communication (LA-ISAC) networks. As a core component of these networks, unmanned aerial vehicles (UAVs) have witnessed rapid proliferation in recent years. However, due to the lag in traditional industry regulatory norms, unauthorized flight incidents occur frequently, posing a severe security threat to LA-ISAC networks. To surveil the non-cooperative UAVs, in this paper, we propose a multi-domain supervised contrastive learning (MD-SupContrast) framework for UAV radio frequency (RF) open-set recognition. Specifically, first, the texture features and the time-frequency position features from the ResNet and the TransformerEncoder (TE) are fused, and then the supervised contrastive learning is applied to optimize the feature representation of the closed-set samples. Next, to surveil the invasive UAVs that appear in real life, we propose an improved generative OpenMax (IG-OpenMax) algorithm and construct an open-set recognition model, namely Open-RFNet. According to the unknown samples, we first freeze the feature extraction layers and then only retrain the classification layer, which achieves excellent recognition performance both in closed-set and open-set recognitions. We analyze the computational complexity of the proposed model. Experiments are conducted with a large-scale UAV open dataset. The results show that the proposed Open-RFNet outperforms the existing benchmark methods in terms of recognition accuracy between the known and the unknown UAVs, as it achieves 95.12% in closed-set and 96.08% in open-set under 25 UAV types, respectively.