I have him working again. 
For this, I reset him back to ‘Discobot’ from both the admin and user preference screen (which did not make him work), and then changed his name from his preferences page and made sure to press ‘change’, ‘yes’, and then Save Changes. This has got him responding to a new name again. 
I’m not 100% sure what the crucial fix is, but I’m going to try and break him and fix him again a few times and see if that reveals anything new. 