You cannot rename a skillset that is referenced by an active script. Skillset names are "sticky" (hard to change) and involve script modifications as well. You have two choices:
1) comment out all skillset references in scripts. The skillset name should no longer be grayed out. However, sometimes references in SCCS do not clear without a reboot, and sometimes they don't clear up even with a reboot (in which case the skillset name will stay grayed out. If you can change the skillset name, go back and update the scripts accordingly.
2). Create the new skillset name. Assign agents to the new skillset. Update scripts with the new skillset name. Remove agents from the old skillset name. Delete the old skillset (so no one is assigned to it by mistake.
The moral of the story is: set up skillset names carefully, changing them later is a pain. When possible use CDN names in phoneset displays (instead of skillset names). CDN names can be changed on the fly with none of the issues of changing skillset names.