To update a rule category name in SharePoint, please follow these steps:
Rename “category name" in metadata:
Search “Rules to Better Lync" to find it, double click the “term item title" to rename it to “Rules to Better Skype for Business (formerly Lync)"

Rename “rule summary page" title:
Go to the “Rule Summary page", edit its title with the new name “Rules to Better Skype for Business (formerly Lync)":

Update “rule category field value" for sub-rules:
Use the left navigation to filter and find all the rules under this category. Use the 1<sup>st</sup> “tick icon" to select all of them, then click “
Files " | “
Check Out " to check them out:

Use “Library" | “Quick Edit" to switch to “quick edit" mode:

Update the 1st row with new “category name", then you can use “copy & paste" to update all the rest in one goal.

Check-in and publish all the rules when you finish your modification.
[Optional] Rename “page URL"