Urea is an indispensable nitrogen fertilizer, but its conventional production relies on the highly energy-intensive Haber-Bosch and Bosch-Meiser processes, leading to substantial energy consumption and CO2 emissions. In this study, density functional theory (DFT) combined with a constant electrode potential model was employed to investigate C-N bond coupling on Cu(111) surfaces covered with graphene (Gr), nitrogen-doped graphene (NDG), and defect nitrogen-doped graphene (dNDG). The results reveal that although the coverage of these two-dimensional materials generally increases the reaction free energy, most coupling steps exhibit reduced activation barriers. Among them, NDG/Cu demonstrates the highest catalytic efficiency, followed by Gr/Cu, while dNDG/Cu performs the worst. Charge density difference (CDD) analysis indicates that the variations in efficiency are related to electron transfer between the copper surface and nitrogen species, while interaction region indicator (IRI) analysis shows that additional attractive interactions from the overlayer stabilize the transition state, thus lowering activation energies. These findings not only advance the mechanistic understanding of C-N coupling but also provide theoretical guidance for designing efficient catalysts, paving the way toward sustainable urea synthesis.