The Relativistic Heavy Ion Collider forward (RHICf) experiment aims at understanding the high-energy hadronic interaction by measuring the cross sections of very forward neutral particles in proton-proton collisions at $\sqrt{s}$ = 510 GeV. For the analysis of the photon measurement, the trigger efficiency and the particle identification performance are studied by using the Monte Carlo simulation data and the experimental data. In the RHICf operation, two kinds of trigger modes (Shower, HighEM) were implemented. The trigger efficiency of the Shower trigger is 100$\%$ for photons with the energies more than 20 GeV. The HighEM trigger is designed to detect high energy photons effectively, and the trigger efficiency of the HighEM trigger is 90$\%$ for photons with the energies more than 130 GeV. The correction factor for the photon identification is calculated by using the efficiency and purity. It is found that this correction does not make a sizeable effect on the shape of the energy spectrum because the energy dependency of the factor is small.