You can rename, delete, or edit any keyword groups you've setup for any campaign.
Renaming Keyword Groups
To do this, go the Detailed Monitored Keywords or Keyword Research sections. To get there, you can either select the Monitored Keywords component (Competitors & Keywords/Monitored Keywords) and click on the green Keyword Research button or use a shortcut from the My Sites section (click on My Sites/Sites tab, click on the blue View Campaigns icon, click on the yellow Campaign Options icon and then click on the link to Monitored Keywords).
To rename a group, simply leave your selection highlighted in the dropdown and enter a new name in the box. In the example below, I'm changing the keyword group called "Competitor" to "Marketplace":
Click on Save and you'll notice the keyword group name has changed:
If you're in the Keyword Research task table, clicking on either of the Edit Groups link will also take you through the same process:
Creating New Keyword Groups
If you go through the same process as described above, in order to create a brand new keyword group, you need to ensure that "Select Group" is shown in the dropdown menu (otherwise you will simply end up renaming the group you have selected as described above):
You'll then see a new Keyword Group box in the Monitored Keywords tab:
You'll also notice that the keyword group has become immediately available from the dropdown option in the Keyword Research tab (orange arrow) and it can be used to filter keywords in the table, using the Keyword Groups column (purple arrow):
Moving Keywords from one Keyword Group to another
Again, we've made this pretty simple. From either of the tables in the (Detailed) Monitored Keywords task table or the Keyword Research Suggestions table, simply select the keywords you want to move and use the "Apply to Selected" dropdown at the bottom left of the table. In the example below, I'm moving six keywords from the "Manual" group to the one I've just created called "Brand New Keywords":
A colorbox will pop up. I simply select the new group for these keywords and hit Save:
Now, if I simply click on the blue "8" in the keyword group box, the table will automatically apply a filter to show me just the keywords in that group: