Within Teamwork, you can upload different company logos for each individual company on your site.
Go to the People area of your site and select the Companies tab.
Click the options button (three dots) to the right of the relevant company and select Edit Company.
In the company details modal, go to the Essentials tab and click the blue Edit button below the logo area.
Use the Choose file option to browse files on your computer. You can select GIF, PNG or JPG file formats, and Teamwork will resize it to fit 200 pixels in width.
For more information, see: Adding or Editing a Company