Changing the name of the computer won't have any effect, the users are still the same.
Firstly I was somewhat confused with your first post as my answers related to not being able to update, not really noticing that the error was only related to trying to reinstall.
How did you uninstall ? I'm assuming with add remove programs and that uninstall may have failed in some way, hence the problem in reinstalling.
Try running the avast Uninstall Utility,
find it here, to ensure that all remnants of avast are gone then reboot and try to install avast again. If that is successful we can see if your update problem has either gone or help resolve it.
Follow Techs advice and answer his questions also, that helps us to help you.