I'm assuming if some had a cocktail name tag, you also had your normal nametag; why would you need a sticky label on top of it?
Cocktail nametags are useful when you are mixing with other countries at some kind of social thing where people don't recognize your rank/uniform, but if I really want to know where someone works, I'm sure it will come up during the introductions. Otherwise they are just another bit of unecessary running around when you show up to a unit/new posting, and all of mine have had the unit badge pop off at one time or another, but have never been able to get a backup.