I added some tools to the 'My Tools' folder in my Toolbar. 3 of them appeared but 'Rename' didn't appear. When I refreshed the page, the entire Folder was gone, but when I open Customize, the Folder is there with all 4 Tools.
Usually stuff you don't have rights to should show up, but just be grayed out and won't work. However, if the function isn't relevant to the current page, it may not appear. Try switching to different pages and see if the My Tools menu changes.