Renaming the iPhone should be just like renaming the iPod. You would just click the iPhone under devices, then click the letters in the name of the device as described here:
http://support.apple.com/kb/HT1789
If the iPhone does not show up in iTunes, make sure its directly connected to the Mac using the cable that came with the iPhone. If it still does not show up reinstall iTunes.
http://www.apple.com/itunes/download/
The area that used to say "Tommy's iPhone" is now blank. I am unable to rename it by double clicking the area or right clicking the area. I have renamed many ipods in the past. This one I can't figure out. When it sync it says for example. Synching photos to " ". There used to be Tommy's ipod in between the " ". I have closed and restarted itunes. Closed my iMac down. I even did a complete restore from backup. The only way to be able to rename it would be to completely restore the iphone (Not from backup). That or somehow reinstall the software. I'm not sure. It's really not that big of a deal, its just sort of a mission now (And its annoying not having it named)
You probably hit the space bar while your phone's name was highlighted. If so there is a space instead of a name. Click to the right of the phone symbol, just below and very slightly left of the "e" in "Devices" and see if you highlight a space. If you do, type your phone's name.
Renaming the iPhone follows the same way as renaming a folder. Click where the title of the folder is.
* Click once on the iPhone
* Click once again where the name would be just to the right
** Single click, not double click. **
The flashing bar should show in the name plate where the space is.
ok - I figured it out after 6 months and help from Joe's suggestions
Hold left mouse key down and move your mouse from right to left over immediately to the right of the device picture under devices on the left side.
This will open up a little white box where you can type the name in there.