If a shift knob button breaks or is damaged, there are two options to consider: changing the entire shift knob, or just switching out the button. The best solution depends on your car, the extent of your damage, and whether you are hiring someone to do the work for you or doing it yourself. In many instances, if it is the shift knob button that is damaged, the knob button itself can be replaced. If the damage extends further and affects the functionality of the shift knob in its entirety, it may be the best idea to replace the entire knob, button and all.
For more info, see How to Install an Automatic Shift Knob