When if you will change the widget name in ControllerToolboxItem attribute of your controller, Sitefinity will register another widget with a new name.
If you want to get rid of widget, you can do it in two ways:
1) Edit configuration file manually \App_Data\Sitefinity\Configuration\ToolboxesConfig.configfind and remove line related to old widget
2) Edit settings from Sitefinity backend. Go to Administration -> Settings -> Advanced -> Toolboxes -> Toolboxes -> Page Controls -> MVC -> Tools and delete unnecessary widget