How to rename a Trailhead Playground?

Yes, you can rename trailhead playground by following these steps,

• click the dropdown and click Manage my hands-on orgs
  
• click the Pencil icon next to one of your Trailhead Playgrounds to rename it, or the X icon to disconnect it. To connect a Trailhead Playground or Developer Edition org, click Connect an org.
  

For more detailed info read Connecting, Disconnecting, and Renaming Trailhead Playgrounds.

Additional: what is trailhead playground?

A Trailhead Playground is an org you can use to complete hands on challenges and try out new features and customizations. Much like a real playground, a Trailhead Playground lets you play around and make customizations without impacting anything else (in this case, your production org).