Are there Dark Stars In the visible universe, we have a lot of matter to energy conversion going on in stars.  Is there an equivalent structure that is converting dark matter to dark energy?
Dark matter has different properties than ordinary matter. It cannot collide, and thus it alone cannot coalesce to form a star. Furthermore, dark matter and dark energy are unassociated properties. There is not currently any reason to assume dark matter can be converted to dark energy.

That said, there is a strictly hypothetical entity referred to as a dark star, which does involve dark matter. While composed mostly of ordinary matter, this entity is hypothesized to include a high concentration of dark matter, generating heat and preventing fusion of the ordinary matter. If dark stars existed, it is likely they existed in the early universe and did not survive to the present. They are modeled to be large clouds--4 to 2000 astronomical units in diameter--of hydrogen and helium, with a surface temperature low enough to make them invisible to the naked eye.