Copy and change item names in chest
Does this need to happen particularly quickly? Because if not, you could summon tnt or a fireball to destroy the cloned chest so it drops its items, use /entitydata to change their display names, then teleport them to a hopper above another chest. This is a comparatively slow workaround and leaves you with an extra chest (the cloned one that was destroyed will drop as an item), but you can't edit an item's data without completely overwriting it unless it's in entity form. Hope this helps!