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Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant challenges, particularly when it comes to complex 3D patient-specific shapes in the real world. First, it is notoriously challenging to parameterize the input space of arbitrarily complex 3-D geometries. Second, the process often involves massive forward simulations, which are extremely computationally demanding or even infeasible. We propose a novel deep learning surrogate modeling solution to address these challenges and enable rapid hemodynamic predictions. Specifically, a statistical generative model for 3-D patient-specific shapes is developed based on a small set of baseline patient-specific geometries. An unsupervised shape correspondence solution is used to enable geometric morphing and scalable shape synthesis statistically. Moreover, a simulation routine is developed for automatic data generation by automatic meshing, boundary setting, simulation, and post-processing. An efficient supervised learning solution is proposed to map the geometric inputs to the hemodynamics predictions in latent spaces. Numerical studies on aortic flows are conducted to demonstrate the effectiveness and merit of the proposed techniques.