JOSM should have a .desktop file for KDE/Gnome/etc
It is standard for GUI apps to have a .desktop file so the GUI environments can list it in the menu. The attachment is a starting point; the Name entry needs to be L10N'd into more languages, but it works and is a starting point. The osm_logo.png that I use on my system was just downloaded from the OSM home page; this needs to be vetted for copyright, but presumably is "OK" as JOSM is now part of OSM??