firefox 108 supports --class since 2012:
check the class:
$ xprop [...] WM_CLASS(STRING) = "Navigator", "FxMogic"
.desktop menu entry:
$ cat ~/.local/share/applications/menulibre-firefox-mogic.desktop [Desktop Entry] Version=1.1 Type=Application Name=Firefox Mogic Comment=Firefox with Mogic company profile Icon=firefox-symbolic Exec=firefox -P mogic --class FxMogic %u Actions= Categories=WebBrowser;X-GNOME-WebApplications; MimeType=text/html;text/xml;application/xhtml+xml;application/xml;x-scheme-handler/http;x-scheme-handler/https;x-scheme-handler/ftp;x-scheme-handler/chrome;application/x-xpinstall; StartupWMClass=FxMogic