The conflict may arise when you unplug the printer, assuming that you ever do.

With recent Windows versions you should have an icon in the System Tray, at the bottom right side of the window, that looks like a little "block" with a fat arrow above it. This is the "safely remove" utility. A "proper" name would be it's the "device dismount" button.

If you don't go there, double click the icon to get the menu of devices, and click on the device you want to remove, before you pull the plug, your system thinks that device is still connected, at least until you reboot. If you plug the device back in, the computer thinks "the old one is already there, so this must be a new one, I guess I should install it."

With some ancient versions of Windows, you had to go to control panel to "unattach" a device, so most people just shut the computer down before unplugging anything. That way the computer's PnP routine looked, at reboot, to see what was actually connected, and didn't get tricked into thinking you had more junk hooked up than was really there. The "dismount button" probably appeared fairly recently in response to complaints from the "road warriors" who do a lot of hooking and unhooking to their laptops, but it's helpful for desktop units as well.

There could be other problems with your driver installations for the printer, but my guess is that you're just confusing the OS with improper disconnects. If you don't have the "safe remove" button, you can try turning the computer off to remove and/or connect the printer, and see if it recognizes it correctly at reboot without reinstalling new drivers.

If that works, you may be able to install a current "Windows default driver" to create the button, which should remain if you uninstall that driver and put your "real HP" one back on. Success here is "variable."

John