To change your profile username, go to your profile page by clicking on your avatar in the top right corner, and then you can change you name below:
If you want to change your display name, you'll need to click the "Manage Account" option when you click your avatar in the top right corner, and then you can change it from the Atlassian ID settings.
To change a workspace name, or shortname, go to the workspace page (you can do this by selecting the workspace you want from the workspace menu at the top toolbar on Trello).
And then select the pencil next to the workspace name.