I cannot change the name of a file/directory on the desktop through right click on the icon. The name becomes selected, but I cannot type in it. This has also happened in the past with some versions of Ubuntu. Is this a bug, or am I not doing it correctly?
To change the name on Ubuntu (unlike OS X) you need to right-click and then choose 'rename'. If you then cannot type to change the name, that's a bug. As a workaround you could try then left-clicking on the name to see if that puts focus in the right place.
It could be that you're hitting the problem described in gnome bug 646900, which is fixed upstream and should be fixed in Ubuntu in a bit. That bug reports suggests some workarounds.
If that doesn't sound like your bug, I suggest you report it by running in the Terminal:
Are you using focus-follows-mouse on Unity? If yes, you can only rename the desktop icons by if there are no applictions open on the desktop. It's a bug: https://bugs.launchpad.net/ubuntu/+source/unity/+bug/889145