Hi Everyone! Thanks for all the feedback on this. I’m on a PC running Windows 10. I have just disabled all my Add-ons and restarted Blender. Same problem with F2. I can get Ctrl F2 to bring up the Batch Rename window, but plain old F2 does nothing. Just to be clear: I have the Armature selected in Object Mode, then go to Edit Mode, select the specific bone I want to rename, press F2 and a Rename Window should appear, right?
Here is snapshot of the Key-Binding for F2:

For the issue of duplicating bones and creating a parent relationship, I unparented everything and now when I duplicate bones they don’t parent anything. Not sure what was happening earlier there.
-Scott