Have black holes ever moved? How did that move?

If you mean black holes in astronomy, the answer is of course yes.

We know that everything in the world is not absolutely moving or absolutely static, but moving or static relative to other objects. In this sense, any black hole is always moving relative to some other celestial bodies. Just as the earth moves with respect to the sun, so does the sun with respect to the Milky Way. In fact, most of the black holes we talk about are formed by the collapse of stars, and their trajectories are usually basically the same as those of the stars that form them. Of course, due to the process of supernova explosion in the process of black hole formation, violent explosion may cause minor changes in orbit, but it will be close.

If what you say is similar to the rotation of the earth, black holes certainly exist, although not all black holes exist. But it is almost certain that another black hole formed by the collapse of a star with rotation must also have rotation, at least at the beginning of its formation. In fact, scientists have a clear understanding of this rotating black hole through calculus. According to calculation, its rotation will release gravitational waves, which will cause its energy loss, make it turn slower and slower, and finally stop turning. But the process of black hole rotation will definitely be a stage that most stars collapse to form black holes.