Description of problem: When you start the Wayland version of FF, GNOME thinks that Firefox is the "usual" Firefox, because Firefox itself sets the WMClass to "Firefox" or so.
Version-Release number of selected component (if applicable):
Steps to Reproduce:
1. Pin Firefox to Wayland to your favorites (pane) in GNOME.
2. Click on it.
It will start and soon a new entry in your pane will appear with a Firefox logo only labeled "Firefox" instead of "Firefox for Wayland".
Start and keep the icon it used to start. It should be controllable via the existing icon (for minimizing etc.) and not use a new one.
E.g. Tor Browser had the same problem.
* In the .desktop file, you can add StartupWMClass to describe what class it should be using when starting.
* Note that this will be overridden by Firefox later, so you may want to add the "--class <startupclass>" to the command line arguments of Firefox. Then Firefox knows what class to use.
IMHO you may just let it use the default Firefox class. In this case adjusting the desktop file should be enough.
A dupe of Bug 1585369.
*** This bug has been marked as a duplicate of bug 1585369 ***