One way you can do this is to move all the games to a newly created category and delete the old one (A category is deleted when no games are inside of it). You can do this by:

1. Select all the games in the category:
   • Control click on all the ones you want
   • Shift click the top and the bottom one
2. Right click on the selected games
3. From the list select "Set Categories..."
4. In the new window create the new category
5. Add the games to the new category and remove them from the old one

Another way to do this is to change the settings file. Before altering this file make sure to close and exit steam. The file is located where steam is installed, in my case it is:

C:\Program Files (x86)\Steam

From this root it is located at:

root\userdata\<userid>\7\remote\sharedconfig.vdf

Where <userid> corresponds to the users library you want to update. Open this file in notepad, or better yet notepad++. You then need to find and replace all examples of the category surrounded by quotes.

For example, if I wanted to rename the category Want to play to Meh I'd find on "Want to play" and replace with "Meh".

Once you've made all the relevant changes to the file, save it and open steam again.