Pin to taskbar icon gets (2) appended

After some research, I found a hidden folder

%appdata%\Microsoft\Internet Explorer\Quick Launch\User Pinned

I had searched around here, thinking that Quick Launch and Taskbar pinning were very much the same, but I hadn't seen it because it was hidden. In that folder, there was a shortcut with the desired name. Why that shortcut didn't appear on the taskbar, I don't know. I deleted that shortcut, then re-pinned the application, and it now appears with the correct name.

The answer is indeed found in the C:\Users\(USERNAME)\AppData\Roaming\Microsoft\Internet Explorer\Quick Launch\User Pinned\Taskbar...

However I resolved the problem by checking the Properties of the icon in question (that even there wouldn't allow itself to be renamed). In my case, the icon was referencing an obsolete directory where I'd previously installed the application (Mozilla Firefox). For some reason that icon wasn't removed from my user profile and thus tainted every icon I tried to place on the taskbar. Once I changed the Target: and Start In: directories, the name of the icon changed without a hitch.