Within Teamwork, you can edit existing categories and update their names and associated color.
Categories can be found in the left-hand pane in the Messages, Files, Notebooks, Links and Projects list areas.
To edit a category in one of these areas, hover over the categories pane to reveal the settings cog.

Within the Managing Categories modal, you will see an edit pencil icon and trash can icon to the right of each category name.
Click the edit pencil icon to update a category.

The Edit Category modal will allow you to update the category name and color.
You also have the option to move the category to a top level or sub-category via the drop down menu.
Note: Subcategories can go up to three levels deep.

Click Update Category to save your changes.
For more information, see: Changing a Project Category