Yes, a dispenser's main task is to dispense out the liquid in it, in this case, hand sanitizer. Irrespective of the brand of the sanitizer you can go ahead and choose whichever sanitizer you would prefer. And still expect that nothing to be different. Although you should keep an eye out for what is the best option for your dispenser as well as if there is any specific type of sanitizer it caters well or better to. For example, some dispensers work best with liquid sanitizers whereas others with the gel ones. So, keep this in mind while getting your sanitizer and dispense as much as you keep track of the brand of the sanitizer.