File etc/emacsclient.desktop contains the following line:

StartupWMClass=Emacsd

This depended on an associated setting in etc/emacs.service, but that setting was removed because it caused problems for things that rely on invocation-name.  See https://debbugs.gnu.org/cgi/bugreport.cgi?bug=37847#54 for more details.

Attached is a patch to set StartupWMClass back to Emacs.

-- 
Peter Oliver