Hide App Name in Mac OS X Lion Dock
You're going to need the Developer Tools installed to do this, so that you can open up .plist files in the Property Editor.

You can edit the com.apple.dock.plist file that is stored in /Users/&lt;username&gt;/Library/Preferences to get rid of all names of persistent applications (e.g. icons that stay in the dock even when you've quit out of them). In-depth instructions are here, on the apple developer website.

Note that I tried the "without dev tools" instructions at the above link and the .plist file was full of non-human-readable encoded data, so you may have a harder time if you don't have the Property Editor or Xcode applications installed.