What determines the color gamut of a display?
The physical imaging elements of your monitor define your gamut. So things like how bright the elements can be as well as the color spectra of the color elements define the gamut. But, thats quite the simplification, its also affected by such things as the screen surface material and background lighting conditions.

Can the gamut be changed? Sure, if you want a smaller gamut then you can restrict your colors to a subrange of your gamut.