Drag the initial object the the Symbols Panel to create a symbol. This will also convert the original object to a Symbol Instance.
When you want duplicates, drag/drop from the Symbols Panel to place additional instances, or you can merely copy the existing instance on the artboard.
To edit... double-click the Symbol in the Symbols Panel. It will open in an Symbol Editing Mode (basically an Isolation Mode). Make your changes and then use the arrows across the top of the document to exit the editing mode.
All instances of the Symbol will be updated to reflect any edits to the Symbol itself.
More information on working with Symbols can be found in the Adobe Help Files.