Ok, it just happened to me with Dropbox.
Think I've found a workaround:
You need to rename the executable file not the app.
Here's what I've done:
Rename the app "Opera12"
Right click and 'show package contents' > Contents > MacOS
In there is the executable file - rename that "Opera12"
I did some other stuff with profiles while I was messing around so it may be slightly more complicated than that. Let me know if it doesn't work.
It may break your links or have other consequences, but works fine for me.