I have removed and re installed Copper a couple of times on my Mac and it always requires me to make a new password and user when I have reinstalled it.
To Uninstall I put the application Copper in the trash, then go to User/Library/Application Support/ and move the folder Copper to the trash and the folder NCH Software to the trash. Then go to the Preferences folder in the same Library and move com.nchsoftware.copper.plist to the trash. Empty the trash and it should be gone.
That is everything I could find belonging to NCH on my computer and it seems to work for me... YMMV
Good Luck!
Edit: I use a program called Amnesia and I just tried it and it found all the same files and removed them.... You have to pay attention because it will find everything with "copper" in the file name like copperplate.tt which is a font on my system. After using it I had to reenter the user and password just like it had never been installed...