I suggest a context menu for the items on the menu.
On it, I have the following:
1. Rename -- Change the name that is shown to you.
2. Hide From Menu -- Removes the item from the menu.
I also suggest a new button on the menu, "Show All", which only appears if you have at least one hidden item.
3. Show On Menu -- Makes the item not hidden anymore. Only shows if the item is hidden, and you click Show All and find the context menu of the item you want.
Also, being able to change the order of the files and have that new order be persistent would be really helpful.