Think of the individual photons as different locations where a single universal wave function has high density, not as distinct particles. The idea that they are distinct only holds while those locations don't interact and interfere significantly.

Once they interact, the resulting waveform will have other regions of high density. Mapping one of them back to one of the original ones and saying this new photon is the "same" as that original photon is something that might make your brain understand it better by pretending they are Newtonian objects. But it's just a model for understanding, and the further the interaction is from Newtonian collisions the more wrong it will be.