The simplest way to change the name of the Slingbox in the directory is to reconfigure the video input.
The process can be found in this article (follow the section: "To re-specify the AV device from Slingplayer for Desktop").
After you click "Reconfigure Video Input" and "Change Device", it allows you to change the name of your Slingbox. After that, just respecify your zip code, cable provider, and make/model cable box.
Just make sure you have a video signal (i.e. your cable box is powered on) before you reconfigure the input, and you shouldn't have any problems.
Hope this helps!