That's why I clarified if it's just the title of the add-on. If so, you just edit that in addon.json. This file doesn't store an add-on's ID.
If you want to change the ID, you need to be very careful and I wouldn't totally recommend it. You may be able to get away with uninstalling the add-on, renaming the directory and then reinstalling it. (If this is an add-on in use by people already though, this will likely cause some difficulties.)