Using first-principles calculations, we systematically investigated the hydrogen evolution reaction (HER) potential of 27 types of homogeneous dual-atom M₂-N₆-graphene catalysts. Shared nitrogen atoms between dual metal atoms were identified as crucial adsorption sites for hydrogen atoms. Notably, we found that relying solely on the free energy of hydrogen adsorption ( ${\mathrm{\Delta }G}_{{\mathrm{H}}^{\ast }}$) could exclude the extremely unfavorable substrates, but may lead to misleading assessments of HER activation for substrates with modest ${\mathrm{\Delta }G}_{{\mathrm{H}}^{\ast }}$. Thermodynamic activity evaluation reveals that M₂-N₆-graphene (M = Cr, Co, Ni, Cu, Os, Pt) models exhibit promising HER activities. Kinetic analysis, based on the Volmer–Tafel mechanism, determined that the hydrogen coverage and relative distance between the adsorbed hydrogen atoms in the Tafel step affect the reaction energy barrier significantly. The coverage limits depend on the reaction free energy of the non-spontaneous third hydrogen adsorption step. By integrating the kinetic metric with thermodynamic assessments, we propose that the Co₂-N₆-graphene model displays superior HER activity. We further recommend selecting one of the metal positions in M_aM_b-N₆-graphene to be Cr and excluding Cu and Ni elements during the selection of the second metal atom when designing heterogeneous M_aM_b-N₆-graphene for alkaline HER catalyst. This study establishes a convenient workflow and provides valuable insights for the rational design of efficient HER catalysts.