Hey Cheyenne R., are you thinking of an icon within Slack workspace or on the companion forums site?
Within Slack:
Slack itself doesn't have native "icons" next to names like how other platforms display badges, but I have seen other workspaces upload a company emoji (like ) and encourage employees to include the emoji in their status alongside the name of the company.
You also have the option of using Tightknit to create a profile photo frame which you can award to all your employees. Your employees can then use this to generate a new profile picture with a visual indicator of your company.