How to add a custom field to menu or menu widget in admin

I have different sidebar in different pages. They have different styled custom menu assigned via custom menu widget. Now i just want a unique id to assign each menu or widget to apply the appropriate style to them.

I know there are automatic unique id assigned to each widget and menu. But i don’t want to depend on them as they will change when i move my code to another server.

Example: I have “green menu” in 5 different pages. When using custom menu or custom menu widget just want a field to enter text “green-menu”. So that there could be different “green-menu” container id to recognize.