Cognitional heart disease is one of the leading causes of mortality among newborns. Tissue-engineered vascular grafts offer the potential to help treat cognitional heart disease through patient-specific vascular grafts. However, current methods often rely on non-personalized designs or involve significant human intervention. This paper presents a computational framework for the automatic shape optimization of patient-specific tissue-engineered vascular grafts for repairing the aortic arch, aimed at reducing the need for manual input and improving current treatment outcomes, which either use non-patient-specific geometry or require extensive human intervention to design the vascular graft. The paper's core innovation lies in an automatic shape optimization pipeline that combines Bayesian optimization techniques with the open-source finite volume solver, OpenFOAM, and a novel graft deformation algorithm. Specifically, our framework begins with Laplacian mode computation and the approximation of a computationally low-cost Gaussian process surrogate model to capture the minimum weighted combination of inlet-outlet pressure drop (PD) and maximum wall shear stress (WSS). Bayesian Optimization then performs a limited number of OpenFOAM simulations to identify the optimal patient-specific shape. We use imaging and flow data obtained from six patients diagnosed with cognitional heart disease to evaluate our approach. Our results showcase the potential of online training and hemodynamic surrogate model optimization for providing optimal graft shapes. These results show how our framework successfully reduces inlet-outlet PD and maximum WSS compared to pre-lofted models that include both the native geometry and human-designed grafts. Furthermore, we compare how the performance of each design optimized under steady-state simulation compares to that design's performance under transient simulation, and to what extent the optimal design remains similar under both conditions. Our findings underscore that the automated designs achieve at least a 16% reduction in blood flow pressure drop in comparison to geometries optimized by humans.