Click the General tab instead, and you'll see the library name. Enter a new name here and click OK.
Note that this is not the name of your Mac, as defined in the Sharing pane of OS X's System Preferences. If you wish, you can use the same name, but iTunes picks the user's name--Kirk McElhearn's Library, for example--by default to distinguish among what may be several libraries available on a Mac with multiple users.
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