How to cleanly rename an OctoPrint plugin

I recently found out there is another plugin that has the same display name as mine and I figured I can rename mine to remove any potential confusion. What is the correct way to rename a plugin with minimal disruption to folks who have already installed it?

To be honest, switching the plugin_name (, __plugin_name__ ( and displayName (software update hook) is the least impactful. I did that for what's now called Cura Thumbnails plugin, but I kept the plugin_identifier the same. That way the plugin could still properly update versions, etc. it just changed what is shown in Plugin Manager and also in Software Update, Settings, etc. assuming you have changed the name right.