Purpose: Laparoscopic ultrasound (LUS) enhances the safety of liver surgery by visualizing intrahepatic vessels in real-time. Still, vessel identification remains difficult due to probe constraints, complex vascular structure, and tissue deformation. This work aims to enable real-time, patient-specific vessel identification that remains robust under deformation through deformable ultrasound augmentation. Methods: Preoperative CT vessel annotations are used to generate synthetic ultrasound data via optimized physics-based rendering, coupled with domain adaptation to intraoperative ultrasound. The rendering is trained end-to-end for vessel identification and patient-specificity, eliminating the need for preoperative ultrasound. A deformation-aware augmentation simulates realistic intraoperative motion and tissue deformation within the rendering pipeline. Results: In abdominal phantom and limited clinical feasibility experiments (single-case clinical evaluation), the framework achieved real-time intrahepatic vessel-branch identification, maintaining performance under new patient poses. Conclusion: The framework enables real-time vessel identification without preoperative ultrasound and supports technical feasibility, but multi-patient validation is still needed for generalizability and clinical feasibility.