What Ubivis said... and your F2 isn't working because you have F lock on. Turn F lock off.
F lock on is F2 is undo, F3 us redo, F4 is new etc
If you have done everything, then this is the most bazar thing in the world.
Try and change your theme etc, heck can you take some screenshots or make a vid.
Can you edit it in properties...
There are at least 4 or so ways to rename it.
click layer and F2
Click layer and rename
In layer properties click layer0 and edit box will appear.
Oh, four click layer0 and hit pencil.