You should use an own account for each user. Everything else is insecure.
If you do not want to follow this security instruction you could still use a different JOSM preference directory for each user with the java command line option -Djosm.home="path" or reset the preferences to defaults with JOSM command line option --reset-preferences (untested). See command line option.
Within JOSM you still can use an option with OAuth to only use the token for the current session and not to save it to preferences.
By the way, you should always use OAuth as passing you credentials to the OSM-Server unencrypted is insecure.
Think you have many options.
