I sympathise with your frustration, but perhaps I can shed a little light on what's happening here.
The short answer is that the module names are all the same but the type (far right) column uniquely identifies them.
Joomla! uses the name of the module (title) to label the menu when viewed through the browser and show title (yes) is checked.
If you are not using the module name on the browser (show title (no)), then you can change the module name for your own ease of use.
But, if you want to see Main Menu on the mobile browser then don't change the module name. If you want the imode browser people to see "Imode Main Menu" then go ahead and rename the module, your call.
I have noticed that Joomla! will reorder the modules in module manager using the position column, so for example all the iphone modules are together. This helps to identify which main menu is which.
But, just to add to your pain
on the Main menu module there is a parameter which you can use to choose a different menu name so you can have a main menu with items just for the mobile browser. See my reply to this post.
www.mobilejoomla.com/forum/topic.html?id=428
Hope this is helpful.