Why is it not possible to change username on an Exchange account of Mail.app? I'm trying to set up an Exchange server in Mail.app. The username in the preferences is incorrect, and I can't connect to the server because of that. 

There's no explanation in the UI, or any help section to explain. 

When I select the "User Name:" field nothing happens. The text is gray, and not editable. The same is true for "external server". 

How can you edit this information?
Maybe this is because you are connected to that Exchange server.
You could try to disconnect from it by taking that account offline (Mailbox -> Online Status -> Take "YourAccountName" offline) and try to edit the account then.

If that does not help, try to delete that account and create it again with the corrected credentials.