This may end up being a bit of an overkill solution to achieve it, but you could use the Name Panel Addon (available in Free and Commercial flavors) to rename your active object.
It's a great addon and I strongly recommend it's use, though it may over complicate in this case, because the addon is a lot more complex and is mainly concerned with batch naming and name copying, among other involved functionality.
It does not assign one hot key by default as far as I know, but you can go to the user preferences and manually assign it yourself.
Just browse to the File > User Preferences > Input > 3D View >3D View Global and add a new operator wm.batch_name with the desired key combination.
It should call out the operator popup with the (potentially overly complex) popup dialog