When changing the name on a 'My ITIL Homepage' in order to "duplicate" homepages for users, the dropzones do not copy over.
Release or Environment
Drop zones are unique to the sys_ID of the homepage.
Dropzones will need to be manually recreated and attached to the new homepage, or you can export them via list view and change the sys_ID of the 'page' display_value to the sys_ID of the newly created homepage. To export the dropzones, right-click the 'Page = ...' part of the related list and open in a new window, then export.