Dark matter as far as gravitational forces go , has the same behavior as normal matter. That is how it was discovered and defined. By balancing gravitational forces in the motion of galaxies etc, it was found that more matter was needed than the matter estimated from the luminosity of the bodies. It was observed that the trajectories would not fit the newtonian calculations for trajectories unless more unseen mass was in existence. It was called dark matter.
So dark matter will behave gravitationally as normal matter around a black hole.
Dark energy is a totally different story, the "dark" part copying the dark mass terminology has to do with our mathematical definitions of spacetime in cosmological models , so that they fit the observations of the expanding universe.
Seen as "energy" :
In physical cosmology and astronomy, dark energy is a hypothetical form of energy which permeates all of space and tends to accelerate the expansion of the universe.1 Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate.
So it partakes of the definition of space where the black hole is embedded, and nothing in particular can happen that does not happen around any other tightly bound celestial body, i.e. an observation that clusters of galaxies are moving away from each other. Black holes are within galaxies, and dark energy is so small that it does not disturb the gravitational status within the galaxies and even the cluster of galaxies.