[EvaH (OP)]

Marcus asks:

We know that there is antimatter and we know that there is dark matter, is there anti dark matter?

What do you think?

[Janus]

It's not outside the realm of possibility.   Neutrinos are a type of "dark matter", as they have mass, but do not interact electromagnetically. There are both neutrinos and anti-neutrinos.

[evan_au]

is there anti dark matter?

Some astrophysicists are searching for highly energetic photons (eg Gamma Rays) that might come from annihilation of Dark Matter particles in the center of dwarf galaxies, or near the core of our own galaxy.

But we have no confirmed theory of Dark Matter, so we don't know if this annihilation is possible. Experiments with the Fermi telescope have placed upper limits on how often Dark Matter annihilation could occur.
See: https://www.frontiersin.org/articles/10.3389/fphy.2017.00003/full

There are both neutrinos and anti-neutrinos.

Actually, it is currently unresolved whether neutrinos and anti-neutrinos are distinct particles; they could be the same particle (a Majorana Fermion).
- Neutrinos interact so rarely with anything that it is really hard to interact a neutrino with another neutrino (and measure the result).

There is a precedent for this: Photons are their own anti-particle.

See: https://en.wikipedia.org/wiki/Majorana_fermion