Within Teamwork, you can change the category associated with a project.
Click the three dots to the right of the project name and select Edit project details from the Manage Project tab.

In the Edit a Project modal, select the Advanced Options step to access the category settings.
Click the project category dropdown to view and select from the existing categories. Using the checkbox to the left, select the relevant category for the project. You can also create a new category via the Add Category button.

Once you have selected a category, click Update Project to apply the change.
Alternatively, go to the Settings area of the project and select the General subsection.

Under General Settings, you will see a Category option. Hover over the category section and click the edit pencil.

You can choose an existing category from the dropdown or click Manage Categories to create a new one. Click Save to apply the change.

You can also change the project category from the site-level Projects area by dragging projects into a category listed in the panel on the left.
Alternatively, go to the project's Dashboard tab and hover over the category in the details pane on the left.

For more information, see: Working with Project Categories