Add options to Block Name in Views

When you create a block in views, the view itself already has a name (used for administrative purposes) and the block generally also has a title (shown to end-users). So when you want to give the Block a name (under Block Settings, displayed in the admin interface), rather than typing in something new (or repeated), I'd also like the option to use the existing view name or block title.

So I propose adding radio buttons with those options (and also a 'No name' option) as per the following screenshot/mock-up: (obviously the textfield will be hidden when one of the other radio buttons is selected)