Changing the UPC

I have a private label product and i wanted to change the brand name, i was told by someone else that my UPC needs to be mine so i can make the change. When i created my listing many years ago, i did not buy my upc from gs1, as i was not aware of the procedure to get upc codes. Is the correct barcode neccessary to change the brand name of my product and if so can i get my barcode changed to something from GS1.