Like every planet they are in orbit of something or another planet like our solar system every planet revolves around the sun, my question is: what's the name of the planet or object which the sun revolves around; if the sun is stationary or if our galaxy is in motion, around what it is revolving.
As a previous comment states; it is complicated. But in principle the Sun is just one object in a large collection of objects which we call the Milky Way Galaxy. All the objects in this Galaxy orbit the barycentre (or barycenter, if you prefer the American spelling). The barycentre is, essentially, the common centre of mass of the whole galaxy. In the same way the planets in our solar system don't actually orbit the Sun, they orbit the Solar System Barycentre.
As for the Milky Way Galaxy, that too is a member of a larger group of galaxies, and they all orbit their common barycentre.
The Sun, like all other stars in the Milky Way Galaxy, is rotating around the Galactic Center. The Galactic Center is around 25,000 light years away, and it may contain a supermassive black hole. There is a very intense radio source in the center of the galaxy, called Saggitarius A*, which is thought to be the same as the black hole.