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.
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Also, being able to change the order of the files and have that new order be persistent would be really helpful.