Open-set object detection (OSOD) aims to recognize known object categories while localizing previously unseen instances. However, real-world scenarios often involve co-occurring domain shifts and novel object categories. Existing OSOD methods typically overlook domain shifts, relying on source-trained representations that entangle domain-specific style with semantic content, thereby hindering generalization to both unseen domains and novel categories. To address this challenge, we propose a unified framework, termed DecOmpose and ATtribute (DOAT), which disentangles domain-specific style from semantic structure, thereby facilitating generalizable object detection. DOAT employs wavelet-based feature decomposition to separate style information from high-frequency structural details, thus enabling an explicit separation of domain and category shifts. To account for domain shift, the low-frequency components are perturbed within a style subspace to simulate diverse domain appearances. For unknown object discovery, the high-frequency components are utilized to estimate objectness scores via an attribution mechanism that fuses wavelet energy with semantic distance to known-category prototypes. Extensive experiments on standard open-set benchmarks have demonstrated the superior generalization performance of DOAT.