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

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

Edit

Not sure if this is what you want, but to set the name automatically to a specific predefined name you can add another operator wm.context_set_enum with Context Attributes set to `scene.BatchName.customName and Value set to whatever name you want, but I could not do it all (set the name and actual renaming) at once with a single key press. Perhaps with some additional scripting?