Photons are simply their own antiparticles, but aren't called antphotons.
A subatomic particle that is its own antiparticle is called a "Truly neutral particle". It remains itself under the charge conjugation. All charges: electric, magnetic, color, flavor etc, must be zero.
Positronium, the bound state of an electron and a positron (e−, e+) is also truly neutral, so two photons colliding (two photon physics) can produce a positron and an electron. Or other composite particles that are truly neutral, like a proton antiproton, which requires a lot of energy. (I believe particle accelerators can't provide, but it happens in cosmic rays.)
Remember though that photons do not really collide (at least this is extremely rare). Pair production is a little more complicated than that and happens near a nucleus.
Although the photons behave almost as if real, they are technically virtual.