Firstly - The problem seems NOT to have been as 'universal' as I thought.
Secondly - There appears to have been an improvement 'overnight'.
Thirdly - The remaining dual names were for Skype and Foxit products - In the Properties of their shortcuts, it is possible to remove the content of 'comments', which is what appeared as a 2nd name.
Fourthly - ONLY Internet Explorer NOW showed a name in QuickLaunch which was not the same as for Internet Explorer in \Documents and Settings\username\Application data\Microsoft\Internet Explorer\Quick Launch\; BUT the name on the Quick Launch Internet Explorer icon CAN be renamed as desired.
However a residual phenomen - ONE of the shortcuts (to a DOS program) in Quick Launch shows a 'story' rather than a name. If the shortcut is moved to the desktop, its caption is the name I want it to have, but that does NOT show (at all) as a tooltip when the shortcut is in Quick Launch. So instead of a second name, there is no name at all.