To be especially safe, I thought, I completely uninstalled DO8, then rebooted and installed DO9. This leaves a DO8 icon on the desktop.
This is just fyi. I don't really care. I remove the icon from the desktop anyway.
There are a couple of other threads about this already.
To cut a long story short: Use Microsoft TweakUI to rebuild your icon cache. It's a bug in Windows as far as we can tell. Windows doesn't notice that the icon has changed but TweakUI corrects it.