No, not usually. Ghostly phenomena seem tied to locations. If ghosts could go somewhere else, they probably would. (If you had a choice, would you spend relentless years at a site where people ignore you, or are afraid of you? Probably not.)
Exceptions to this rule are rare. One of them is Judith Thompson Tyng. Her ghost moved around Tyngsboro, Massachusetts (USA) for many years. Witnesses say she’s still there, over 200 years later.
According folklore, Judith tormented (and perhaps killed) two 18th century men responsible for her death.
One of them was John Alford Tyng, the father of her child. He killed her and buried her under the hearth of their home.
Then, when Judith haunted him, he moved to another house. Judith’s ghost followed him.
He tried again, with the same results.
Finally, when John Tyng was dying, Judith’s ghost stood at his door and prevented anyone from helping him.
Judith’s other victim was a quack called “Dr. Blood.” He’d pretended to be a minister or a Justice of the Peace and convinced Judith she was married to John. When Dr. Blood was found dead on a country road, Judith’s distinctive boot print was on his back. Folklore claims she’d forced his head into a puddle, and held him there until he drowned.
Of course, stories like those must be studied closely. About 99% of ghosts seem to stay in one place. Anything that moves from one location to another might something else.
For example, poltergeists can follow and torment the people they select as targets. That’s why many researchers don’t believe poltergeists are ghosts.
Demons can follow people or even become attached to them. Demons can mimic ghosts.
Few credible stories describe a ghost changing locations. Even the Bell Witch was probably the product of several entities. Those include at least one opportunistic (and very alive) person in that community.
If you think a ghost has followed you, see a priest or spiritual minister immediately. Chances are, the problem isn’t a ghost. It could be something far worse. You might be at risk.
Don’t seek help from strangers, online. Not even me. Find a priest or full-time minister to help you, even if you are not a religious person or a member of that congregation. (A good minister won’t care. His or her job is to help with spiritual matters, period and full stop.)