Right now Rename and Batch Rename has separate operators and shortcuts (
Ctrl+F2 respectively). You can press
F2 on multiple items but it will just rename the first item. You can press
Ctrl+F2 on a single item which does not make sense.
IMO it should be just plain
F2 and blender should intelligently call which operator depending the number of items selected.
For reference this is how Ubuntu does this: