Within Teamwork, you can quickly view the details of the company associated with a project..
You can view the company's information by hovering over the company to the right of the project name.
In the pop up modal, clicking the company name at the top will bring you directly to the full company view in the People section.
You can also view a list of the projects associated with the company here, and click into each one directly from the modal.
For more information, see: Adding or Editing a Company