Ability to name widgets (not title) for the backend

I work on WP e-Commerce sites. I often have to change temporarily to the default Twenty Eleven theme to test that an issue is not related to the 3rd party them I am using. When I switch back to my theme all of the widgets are in the Inactive Widgets area as the theme widget areas differ.
Most of the time I do not title my widgets. Many of my widgets are the same type, i.e. Advanced Text Widget. I then have to open each one, read the code or other content in it and remember where it goes. Add the use of a dynamic widget plugin and this gets evenmore complex as 2 widgets may have the same content but be controlled for display on different pages in different locations.
The addition of a ‘do not display title’ checkbox would help BUT even better would be the ability to name widgets and have it appear in the ‘header’ of the widget where the widget type is displayed. This way I could just take a screen shot of my backend widget layout prior to changing the theme.
To restore the layout I would not have to open the widgets at all.

Even more deluxe but much harder I imagine would be the ability to save and restore widget layouts for different themes